#include <math.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
#include "ran_tg.h"

double ran_tg_zig2000(gsl_rng *r,double a)
{
// Simulate x~N(0,1), subject to x>a, using generator r
// Zig's method

    /* Insert here */
    //****************************
#define N 2001 //total number of vertical boxes
#define I0 1633
#define INVH 815.752794412
#define AMIN -2.00114344036
#define AMAX 2.35814231898

static const double x[2002]={
-2.00114344036, -1.99222497319, -1.98346054064, -1.97484429955, 
-1.96637073844, -1.95803465271, -1.94983112213, -1.94175549031, 
-1.93380334607, -1.92597050637, -1.91825300075, -1.91064705706, 
-1.90314908835, -1.8957556809, -1.88846358309, -1.88126969527, 
-1.87417106036, -1.86716485514, -1.86024838226, -1.8534190628, 
-1.84667442937, -1.84001211972, -1.83342987083, -1.82692551335, 
-1.82049696648, -1.81414223317, -1.80785939563, -1.8016466112, 
-1.7955021084, -1.7894241833, -1.78341119609, -1.77746156789, 
-1.77157377772, -1.76574635972, -1.75997790043, -1.75426703638, 
-1.74861245166, -1.74301287577, -1.73746708152, -1.73197388306, 
-1.72653213402, -1.7211407258, -1.71579858585, -1.71050467618, 
-1.70525799182, -1.70005755945, -1.69490243606, -1.68979170773, 
-1.68472448836, -1.67969991862, -1.67471716482, -1.66977541793, 
-1.66487389256, -1.66001182608, -1.65518847772, -1.65040312776, 
-1.64565507668, -1.64094364448, -1.63626816986, -1.63162800963, 
-1.62702253797, -1.62245114586, -1.61791324043, -1.61340824445, 
-1.60893559571, -1.60449474653, -1.60008516328, -1.59570632588, 
-1.5913577273, -1.58703887321, -1.58274928148, -1.57848848179, 
-1.5742560153, -1.57005143419, -1.56587430138, -1.56172419013, 
-1.55760068375, -1.55350337529, -1.54943186718, -1.545385771, 
-1.54136470719, -1.53736830473, -1.53339620096, -1.52944804125, 
-1.52552347883, -1.52162217451, -1.51774379647, -1.51388802008, 
-1.51005452762, -1.50624300816, -1.50245315732, -1.49868467709, 
-1.49493727566, -1.49121066726, -1.48750457195, -1.48381871552, 
-1.48015282929, -1.47650664995, -1.47287991948, -1.46927238493, 
-1.46568379834, -1.4621139166, -1.45856250129, -1.4550293186, 
-1.45151413918, -1.44801673807, -1.44453689451, -1.44107439192, 
-1.43762901774, -1.43420056334, -1.43078882395, -1.42739359852, 
-1.42401468965, -1.42065190353, -1.4173050498, -1.4139739415, 
-1.41065839498, -1.40735822984, -1.4040732688, -1.40080333771, 
-1.39754826538, -1.3943078836, -1.39108202703, -1.3878705331, 
-1.38467324203, -1.38148999669, -1.37832064258, -1.37516502777, 
-1.37202300283, -1.36889442077, -1.36577913701, -1.3626770093, 
-1.3595878977, -1.35651166448, -1.35344817415, -1.35039729333, 
-1.34735889075, -1.34433283722, -1.34131900553, -1.33831727047, 
-1.33532750874, -1.33234959894, -1.32938342152, -1.32642885875, 
-1.32348579467, -1.32055411507, -1.31763370742, -1.31472446089, 
-1.31182626628, -1.308939016, -1.30606260401, -1.30319692583, 
-1.30034187851, -1.29749736055, -1.29466327193, -1.29183951404, 
-1.28902598968, -1.28622260301, -1.28342925955, -1.28064586614, 
-1.27787233091, -1.27510856325, -1.27235447382, -1.2696099745, 
-1.26687497836, -1.26414939967, -1.26143315384, -1.25872615742, 
-1.25602832809, -1.25333958461, -1.25065984684, -1.24798903567, 
-1.24532707305, -1.24267388194, -1.24002938632, -1.23739351113, 
-1.23476618228, -1.23214732667, -1.22953687208, -1.22693474724, 
-1.22434088179, -1.22175520624, -1.21917765197, -1.21660815123, 
-1.21404663711, -1.21149304353, -1.20894730522, -1.20640935771, 
-1.20387913733, -1.20135658117, -1.1988416271, -1.19633421372, 
-1.1938342804, -1.19134176719, -1.1888566149, -1.186378765, 
-1.1839081597, -1.18144474185, -1.17898845498, -1.17653924329, 
-1.17409705162, -1.17166182545, -1.16923351089, -1.16681205467, 
-1.16439740412, -1.16198950719, -1.15958831239, -1.15719376885, 
-1.15480582623, -1.15242443478, -1.15004954532, -1.14768110917, 
-1.14531907824, -1.14296340494, -1.1406140422, -1.13827094349, 
-1.13593406277, -1.1336033545, -1.13127877363, -1.12896027562, 
-1.12664781637, -1.12434135227, -1.12204084019, -1.11974623744, 
-1.11745750178, -1.11517459142, -1.11289746501, -1.11062608163, 
-1.10836040079, -1.10610038241, -1.10384598683, -1.10159717481, 
-1.0993539075, -1.09711614644, -1.09488385358, -1.09265699125, 
-1.09043552216, -1.08821940938, -1.08600861638, -1.08380310697, 
-1.08160284535, -1.07940779603, -1.07721792392, -1.07503319424, 
-1.07285357258, -1.07067902485, -1.06850951728, -1.06634501647, 
-1.0641854893, -1.06203090299, -1.05988122507, -1.0577364234, 
-1.05559646612, -1.05346132168, -1.05133095884, -1.04920534666, 
-1.04708445447, -1.0449682519, -1.04285670886, -1.04074979556, 
-1.03864748246, -1.03654974031, -1.03445654013, -1.03236785319, 
-1.03028365104, -1.02820390549, -1.02612858861, -1.0240576727, 
-1.02199113034, -1.01992893434, -1.01787105776, -1.01581747391, 
-1.01376815632, -1.01172307877, -1.00968221526, -1.00764554004, 
-1.00561302757, -1.00358465253, -1.00156038986, -0.99954021466, 
-0.997524102295, -0.995512028322, -0.993503968515, -0.991499898856, 
-0.989499795534, -0.98750363494, -0.985511393669, -0.983523048516, 
-0.981538576471, -0.97955795472, -0.97758116064, -0.975608171801, 
-0.973638965958, -0.971673521055, -0.969711815217, -0.967753826752, 
-0.965799534149, -0.963848916073, -0.961901951365, -0.95995861904, 
-0.958018898283, -0.956082768452, -0.954150209071, -0.95222119983, 
-0.950295720583, -0.948373751347, -0.9464552723, -0.944540263778, 
-0.942628706274, -0.940720580437, -0.938815867069, -0.936914547125, 
-0.93501660171, -0.933122012077, -0.931230759626, -0.929342825905, 
-0.927458192603, -0.925576841552, -0.923698754726, -0.921823914239, 
-0.919952302341, -0.918083901419, -0.916218693996, -0.914356662729, 
-0.912497790404, -0.910642059942, -0.908789454391, -0.906939956928, 
-0.905093550856, -0.903250219604, -0.901409946726, -0.899572715898, 
-0.897738510916, -0.8959073157, -0.894079114287, -0.892253890832, 
-0.890431629607, -0.888612314999, -0.88679593151, -0.884982463756, 
-0.883171896464, -0.881364214472, -0.879559402728, -0.877757446289, 
-0.875958330319, -0.87416204009, -0.872368560979, -0.870577878466, 
-0.868789978137, -0.867004845678, -0.865222466878, -0.863442827626, 
-0.861665913911, -0.85989171182, -0.858120207536, -0.856351387342, 
-0.854585237615, -0.852821744825, -0.851060895538, -0.849302676413, 
-0.8475470742, -0.84579407574, -0.844043667966, -0.842295837898, 
-0.840550572647, -0.83880785941, -0.837067685471, -0.835330038202, 
-0.833594905057, -0.831862273578, -0.830132131388, -0.828404466195, 
-0.826679265787, -0.824956518036, -0.823236210891, -0.821518332384, 
-0.819802870626, -0.818089813804, -0.816379150185, -0.814670868113, 
-0.812964956006, -0.811261402359, -0.809560195744, -0.807861324803, 
-0.806164778254, -0.804470544889, -0.802778613569, -0.80108897323, 
-0.799401612876, -0.797716521582, -0.796033688495, -0.794353102828, 
-0.792674753864, -0.790998630954, -0.789324723514, -0.78765302103, 
-0.785983513052, -0.784316189195, -0.78265103914, -0.780988052632, 
-0.779327219479, -0.777668529554, -0.776011972792, -0.774357539187, 
-0.7727052188, -0.771055001748, -0.769406878212, -0.76776083843, 
-0.766116872703, -0.764474971388, -0.762835124901, -0.761197323717, 
-0.759561558368, -0.757927819442, -0.756296097584, -0.754666383496, 
-0.753038667935, -0.751412941712, -0.749789195694, -0.7481674208, 
-0.746547608006, -0.744929748338, -0.743313832877, -0.741699852755, 
-0.740087799157, -0.738477663318, -0.736869436525, -0.735263110116, 
-0.733658675478, -0.732056124049, -0.730455447315, -0.728856636813, 
-0.727259684127, -0.72566458089, -0.724071318781, -0.722479889529, 
-0.720890284907, -0.719302496739, -0.71771651689, -0.716132337275, 
-0.714549949853, -0.712969346627, -0.711390519647, -0.709813461006, 
-0.708238162841, -0.706664617333, -0.705092816706, -0.703522753229, 
-0.70195441921, -0.700387807003, -0.698822909002, -0.697259717642, 
-0.695698225402, -0.694138424799, -0.692580308393, -0.691023868783, 
-0.689469098609, -0.687915990549, -0.686364537323, -0.684814731688, 
-0.683266566441, -0.681720034416, -0.680175128488, -0.678631841567, 
-0.677090166602, -0.67555009658, -0.674011624523, -0.672474743492, 
-0.670939446583, -0.669405726929, -0.667873577698, -0.666342992094, 
-0.664813963358, -0.663286484764, -0.661760549621, -0.660236151274, 
-0.658713283101, -0.657191938515, -0.655672110962, -0.654153793922, 
-0.652636980908, -0.651121665466, -0.649607841176, -0.648095501649, 
-0.646584640529, -0.645075251491, -0.643567328245, -0.642060864528, 
-0.640555854112, -0.639052290799, -0.637550168421, -0.636049480842, 
-0.634550221956, -0.633052385687, -0.631555965989, -0.630060956846, 
-0.628567352271, -0.627075146308, -0.625584333027, -0.624094906531, 
-0.622606860948, -0.621120190437, -0.619634889183, -0.618150951402, 
-0.616668371336, -0.615187143254, -0.613707261455, -0.612228720263, 
-0.610751514029, -0.609275637133, -0.60780108398, -0.606327849002, 
-0.604855926657, -0.60338531143, -0.601915997831, -0.600447980397, 
-0.598981253688, -0.597515812293, -0.596051650823, -0.594588763916, 
-0.593127146234, -0.591666792464, -0.590207697317, -0.58874985553, 
-0.587293261862, -0.585837911097, -0.584383798044, -0.582930917532, 
-0.581479264419, -0.580028833581, -0.57857961992, -0.577131618362, 
-0.575684823852, -0.574239231362, -0.572794835884, -0.571351632432, 
-0.569909616045, -0.568468781781, -0.567029124721, -0.565590639969, 
-0.56415332265, -0.562717167908, -0.561282170913, -0.559848326851, 
-0.558415630934, -0.556984078391, -0.555553664473, -0.554124384454, 
-0.552696233624, -0.551269207297, -0.549843300806, -0.548418509504, 
-0.546994828762, -0.545572253975, -0.544150780554, -0.542730403932, 
-0.541311119559, -0.539892922905, -0.538475809462, -0.537059774736, 
-0.535644814256, -0.534230923567, -0.532818098236, -0.531406333844, 
-0.529995625994, -0.528585970306, -0.527177362417, -0.525769797984, 
-0.524363272681, -0.5229577822, -0.521553322249, -0.520149888557, 
-0.518747476867, -0.517346082941, -0.515945702558, -0.514546331514, 
-0.513147965621, -0.51175060071, -0.510354232627, -0.508958857235, 
-0.507564470415, -0.506171068061, -0.504778646086, -0.503387200419, 
-0.501996727005, -0.500607221804, -0.499218680793, -0.497831099964, 
-0.496444475325, -0.495058802901, -0.493674078729, -0.492290298864, 
-0.490907459377, -0.489525556351, -0.488144585888, -0.486764544102, 
-0.485385427122, -0.484007231094, -0.482629952177, -0.481253586545, 
-0.479878130387, -0.478503579904, -0.477129931315, -0.47575718085, 
-0.474385324756, -0.473014359292, -0.471644280731, -0.470275085362, 
-0.468906769484, -0.467539329414, -0.466172761479, -0.464807062021, 
-0.463442227397, -0.462078253974, -0.460715138136, -0.459352876276, 
-0.457991464804, -0.45663090014, -0.455271178719, -0.453912296989, 
-0.452554251408, -0.45119703845, -0.449840654599, -0.448485096353, 
-0.447130360223, -0.445776442731, -0.444423340411, -0.443071049811, 
-0.441719567489, -0.440368890018, -0.439019013979, -0.437669935967, 
-0.436321652591, -0.434974160468, -0.433627456229, -0.432281536515, 
-0.430936397981, -0.42959203729, -0.428248451119, -0.426905636157, 
-0.4255635891, -0.424222306661, -0.422881785559, -0.421542022528, 
-0.420203014309, -0.418864757658, -0.417527249338, -0.416190486126, 
-0.414854464809, -0.413519182182, -0.412184635053, -0.410850820241, 
-0.409517734574, -0.408185374891, -0.406853738041, -0.405522820883, 
-0.404192620287, -0.402863133132, -0.401534356308, -0.400206286716, 
-0.398878921263, -0.397552256871, -0.396226290467, -0.394901018992, 
-0.393576439394, -0.392252548631, -0.390929343671, -0.389606821491, 
-0.388284979079, -0.38696381343, -0.385643321549, -0.384323500453, 
-0.383004347164, -0.381685858716, -0.380368032151, -0.379050864521, 
-0.377734352884, -0.376418494312, -0.375103285881, -0.373788724679, 
-0.372474807801, -0.371161532352, -0.369848895444, -0.3685368942, 
-0.367225525749, -0.365914787229, -0.364604675788, -0.363295188582, 
-0.361986322774, -0.360678075536, -0.359370444049, -0.3580634255, 
-0.356757017087, -0.355451216014, -0.354146019494, -0.352841424747, 
-0.351537429003, -0.350234029497, -0.348931223475, -0.347629008187, 
-0.346327380894, -0.345026338864, -0.343725879371, -0.342425999699, 
-0.341126697137, -0.339827968983, -0.338529812543, -0.337232225129, 
-0.335935204062, -0.334638746667, -0.333342850281, -0.332047512245, 
-0.330752729907, -0.329458500624, -0.328164821759, -0.326871690682, 
-0.32557910477, -0.324287061407, -0.322995557985, -0.321704591902, 
-0.320414160561, -0.319124261375, -0.317834891761, -0.316546049146, 
-0.315257730959, -0.31396993464, -0.312682657633, -0.311395897389, 
-0.310109651367, -0.30882391703, -0.307538691848, -0.3062539733, 
-0.304969758867, -0.30368604604, -0.302402832315, -0.301120115192, 
-0.299837892181, -0.298556160796, -0.297274918557, -0.295994162991, 
-0.294713891629, -0.29343410201, -0.292154791679, -0.290875958185, 
-0.289597599085, -0.28831971194, -0.287042294318, -0.285765343792, 
-0.284488857941, -0.283212834351, -0.28193727061, -0.280662164316, 
-0.279387513069, -0.278113314477, -0.276839566152, -0.275566265712, 
-0.27429341078, -0.273020998985, -0.27174902796, -0.270477495346, 
-0.269206398787, -0.267935735932, -0.266665504437, -0.265395701961, 
-0.264126326171, -0.262857374736, -0.261588845332, -0.260320735639, 
-0.259053043344, -0.257785766135, -0.25651890171, -0.255252447767, 
-0.253986402012, -0.252720762156, -0.251455525912, -0.250190691, 
-0.248926255146, -0.247662216076, -0.246398571526, -0.245135319233, 
-0.24387245694, -0.242609982395, -0.241347893349, -0.24008618756, 
-0.238824862787, -0.237563916797, -0.236303347359, -0.235043152247, 
-0.23378332924, -0.232523876121, -0.231264790676, -0.230006070698, 
-0.228747713982, -0.227489718327, -0.226232081539, -0.224974801424, 
-0.223717875796, -0.22246130247, -0.221205079267, -0.219949204012, 
-0.218693674532, -0.217438488661, -0.216183644235, -0.214929139093, 
-0.21367497108, -0.212421138045, -0.211167637838, -0.209914468316, 
-0.208661627337, -0.207409112766, -0.206156922468, -0.204905054314, 
-0.203653506179, -0.20240227594, -0.201151361478, -0.199900760679, 
-0.198650471431, -0.197400491626, -0.19615081916, -0.194901451932, 
-0.193652387843, -0.192403624801, -0.191155160714, -0.189906993494, 
-0.188659121058, -0.187411541325, -0.186164252217, -0.184917251661, 
-0.183670537585, -0.182424107921, -0.181177960605, -0.179932093575, 
-0.178686504773, -0.177441192144, -0.176196153635, -0.174951387197, 
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1.1888566149, 1.19134176719, 1.1938342804, 1.19633421372, 
1.1988416271, 1.20135658117, 1.20387913733, 1.20640935771, 
1.20894730522, 1.21149304353, 1.21404663711, 1.21660815123, 
1.21917765197, 1.22175520624, 1.22434088179, 1.22693474724, 
1.22953687208, 1.23214732667, 1.23476618228, 1.23739351113, 
1.24002938632, 1.24267388194, 1.24532707305, 1.24798903567, 
1.25065984684, 1.25333958461, 1.25602832809, 1.25872615742, 
1.26143315384, 1.26414939967, 1.26687497836, 1.2696099745, 
1.27235447382, 1.27510856325, 1.27787233091, 1.28064586614, 
1.28342925955, 1.28622260301, 1.28902598968, 1.29183951404, 
1.29466327193, 1.29749736055, 1.30034187851, 1.30319692583, 
1.30606260401, 1.308939016, 1.31182626628, 1.31472446089, 
1.31763370742, 1.32055411507, 1.32348579467, 1.32642885875, 
1.32938342152, 1.33234959894, 1.33532750874, 1.33831727047, 
1.34131900553, 1.34433283722, 1.34735889075, 1.35039729333, 
1.35344817415, 1.35651166448, 1.3595878977, 1.3626770093, 
1.36577913701, 1.36889442077, 1.37202300283, 1.37516502777, 
1.37832064258, 1.38148999669, 1.38467324203, 1.3878705331, 
1.39108202703, 1.3943078836, 1.39754826538, 1.40080333771, 
1.4040732688, 1.40735822984, 1.41065839498, 1.4139739415, 
1.4173050498, 1.42065190353, 1.42401468965, 1.42739359852, 
1.43078882395, 1.43420056334, 1.43762901774, 1.44107439192, 
1.44453689451, 1.44801673807, 1.45151413918, 1.4550293186, 
1.45856250129, 1.4621139166, 1.46568379834, 1.46927238493, 
1.47287991948, 1.47650664995, 1.48015282929, 1.48381871552, 
1.48750457195, 1.49121066726, 1.49493727566, 1.49868467709, 
1.50245315732, 1.50624300816, 1.51005452762, 1.51388802008, 
1.51774379647, 1.52162217451, 1.52552347883, 1.52944804125, 
1.53339620096, 1.53736830473, 1.54136470719, 1.545385771, 
1.54943186718, 1.55350337529, 1.55760068375, 1.56172419013, 
1.56587430138, 1.57005143419, 1.5742560153, 1.57848848179, 
1.58274928148, 1.58703887321, 1.5913577273, 1.59570632588, 
1.60008516328, 1.60449474653, 1.60893559571, 1.61340824445, 
1.61791324043, 1.62245114586, 1.62702253797, 1.63162800963, 
1.63626816986, 1.64094364448, 1.64565507668, 1.65040312776, 
1.65518847772, 1.66001182608, 1.66487389256, 1.66977541793, 
1.67471716482, 1.67969991862, 1.68472448836, 1.68979170773, 
1.69490243606, 1.70005755945, 1.70525799182, 1.71050467618, 
1.71579858585, 1.7211407258, 1.72653213402, 1.73197388306, 
1.73746708152, 1.74301287577, 1.74861245166, 1.75426703638, 
1.75997790043, 1.76574635972, 1.77157377772, 1.77746156789, 
1.78341119609, 1.7894241833, 1.7955021084, 1.8016466112, 
1.80785939563, 1.81414223317, 1.82049696648, 1.82692551335, 
1.83342987083, 1.84001211972, 1.84667442937, 1.8534190628, 
1.86024838226, 1.86716485514, 1.87417106036, 1.88126969527, 
1.88846358309, 1.8957556809, 1.90314908835, 1.91064705706, 
1.91825300075, 1.92597050637, 1.93380334607, 1.94175549031, 
1.94983112213, 1.95803465271, 1.96637073844, 1.97484429955, 
1.98346054064, 1.99222497319, 2.00114344036, 2.01022214438, 
2.01946767679, 2.02888705206, 2.03848774477, 2.0482777311, 
2.05826553511, 2.06846028045, 2.07887174838, 2.08951044301, 
2.10038766485, 2.11151559402, 2.12290738458, 2.134577272, 
2.14654069586, 2.15881444048, 2.17141679688, 2.18436774981, 
2.19768919492, 2.21140519193, 2.22554226128, 2.24012973355, 
2.2552001633, 2.27078982224, 2.28693929054, 2.30369417085, 
2.32110595686, 2.33923309844, 2.35814231898, 2.37791026061, 
2.39862555987, 2.42039149646, 2.443329416, 2.46758321428, 
2.49332530382, 2.52076469056, 2.55015812204, 2.58182581912, 
2.61617424522, 2.65373004265, 2.69519238025, 2.74151706196, 
2.79405848235, 2.85482417228, 2.92696747419, 3.01584090355, 
3.13157463056, 3.29675264228};

static const double yl[2001]={
0.0538676014717, 0.0548354330697, 0.0557991640245, 0.0567588585541, 
0.0577145786948, 0.05866638441, 0.0596143336931, 0.0605584826623, 
0.0614988856508, 0.0624355952904, 0.0633686625906, 0.0642981370127, 
0.0652240665394, 0.0661464977405, 0.0670654758347, 0.0679810447477, 
0.0688932471675, 0.069802124596, 0.0707077173982, 0.0716100648488, 
0.0725092051756, 0.0734051756019, 0.074298012385, 0.0751877508543, 
0.0760744254467, 0.0769580697397, 0.0778387164844, 0.0787163976352, 
0.0795911443789, 0.0804629871627, 0.0813319557199, 0.0821980790956, 
0.08306138567, 0.0839219031814, 0.0847796587481, 0.0856346788892, 
0.0864869895441, 0.087336616092, 0.0881835833697, 0.0890279156891, 
0.0898696368538, 0.0907087701755, 0.0915453384885, 0.0923793641651, 
0.0932108691291, 0.0940398748697, 0.0948664024544, 0.0956904725411, 
0.0965121053906, 0.0973313208777, 0.0981481385023, 0.0989625774004, 
0.0997746563536, 0.1005843938, 0.101391807842, 0.102196916259, 
0.10299973651, 0.103800285749, 0.104598580828, 0.105394638309, 
0.106188474468, 0.106980105304, 0.107769546546, 0.108556813661, 
0.109341921858, 0.110124886098, 0.110905721095, 0.111684441327, 
0.112461061041, 0.113235594256, 0.114008054769, 0.114778456164, 
0.115546811812, 0.116313134879, 0.117077438329, 0.117839734932, 
0.118600037264, 0.119358357714, 0.120114708488, 0.120869101612, 
0.121621548938, 0.122372062145, 0.123120652746, 0.123867332088, 
0.124612111359, 0.125355001589, 0.126096013656, 0.126835158285, 
0.127572446055, 0.1283078874, 0.129041492613, 0.129773271849, 
0.130503235127, 0.131231392331, 0.131957753219, 0.132682327417, 
0.133405124429, 0.134126153634, 0.134845424292, 0.135562945545, 
0.136278726418, 0.136992775823, 0.137705102563, 0.138415715327, 
0.139124622701, 0.139831833164, 0.140537355092, 0.141241196759, 
0.14194336634, 0.142643871912, 0.143342721456, 0.14403992286, 
0.144735483917, 0.145429412331, 0.146121715716, 0.146812401597, 
0.147501477416, 0.148188950527, 0.148874828201, 0.149559117629, 
0.15024182592, 0.150922960105, 0.151602527134, 0.152280533885, 
0.152956987158, 0.15363189368, 0.154305260103, 0.154977093011, 
0.155647398914, 0.156316184255, 0.156983455408, 0.15764921868, 
0.158313480311, 0.158976246478, 0.159637523292, 0.160297316801, 
0.160955632992, 0.161612477792, 0.162267857065, 0.162921776617, 
0.163574242196, 0.164225259493, 0.164874834141, 0.165522971719, 
0.166169677749, 0.166814957701, 0.167458816989, 0.168101260978, 
0.168742294978, 0.16938192425, 0.170020154004, 0.170656989399, 
0.171292435549, 0.171926497516, 0.172559180317, 0.173190488919, 
0.173820428247, 0.174449003177, 0.175076218543, 0.175702079132, 
0.176326589689, 0.176949754916, 0.177571579471, 0.178192067971, 
0.178811224993, 0.179429055072, 0.180045562701, 0.180660752337, 
0.181274628394, 0.18188719525, 0.182498457245, 0.183108418678, 
0.183717083814, 0.184324456881, 0.18493054207, 0.185535343536, 
0.186138865399, 0.186741111744, 0.187342086623, 0.187941794051, 
0.188540238012, 0.189137422456, 0.189733351301, 0.19032802843, 
0.190921457698, 0.191513642926, 0.192104587904, 0.192694296391, 
0.193282772116, 0.19387001878, 0.19445604005, 0.195040839567, 
0.195624420943, 0.196206787758, 0.196787943569, 0.197367891899, 
0.197946636249, 0.198524180089, 0.199100526863, 0.199675679989, 
0.200249642858, 0.200822418835, 0.201394011258, 0.201964423442, 
0.202533658675, 0.20310172022, 0.203668611317, 0.204234335179, 
0.204798894998, 0.20536229394, 0.205924535147, 0.20648562174, 
0.207045556815, 0.207604343447, 0.208161984685, 0.20871848356, 
0.209273843078, 0.209828066225, 0.210381155963, 0.210933115235, 
0.211483946962, 0.212033654044, 0.212582239359, 0.213129705768, 
0.213676056109, 0.2142212932, 0.21476541984, 0.215308438808, 
0.215850352864, 0.216391164747, 0.21693087718, 0.217469492865, 
0.218007014486, 0.218543444708, 0.219078786178, 0.219613041525, 
0.220146213361, 0.220678304278, 0.221209316853, 0.221739253644, 
0.222268117192, 0.222795910022, 0.22332263464, 0.223848293537, 
0.224372889187, 0.224896424048, 0.225418900562, 0.225940321153, 
0.22646068823, 0.226980004189, 0.227498271406, 0.228015492244, 
0.228531669051, 0.229046804158, 0.229560899883, 0.230073958527, 
0.230585982379, 0.23109697371, 0.231606934779, 0.23211586783, 
0.232623775093, 0.233130658784, 0.233636521103, 0.234141364239, 
0.234645190367, 0.235148001646, 0.235649800223, 0.236150588234, 
0.236650367797, 0.237149141021, 0.23764691, 0.238143676816, 
0.238639443537, 0.23913421222, 0.239627984909, 0.240120763634, 
0.240612550416, 0.24110334726, 0.241593156162, 0.242081979103, 
0.242569818056, 0.243056674978, 0.243542551818, 0.244027450511, 
0.244511372982, 0.244994321143, 0.245476296896, 0.245957302131, 
0.246437338729, 0.246916408556, 0.247394513471, 0.24787165532, 
0.248347835939, 0.248823057154, 0.249297320778, 0.249770628616, 
0.250242982463, 0.250714384101, 0.251184835304, 0.251654337834, 
0.252122893446, 0.252590503882, 0.253057170876, 0.253522896151, 
0.253987681421, 0.254451528389, 0.254914438751, 0.255376414192, 
0.255837456386, 0.256297567001, 0.256756747694, 0.257215000112, 
0.257672325893, 0.258128726668, 0.258584204057, 0.259038759672, 
0.259492395116, 0.259945111982, 0.260396911857, 0.260847796317, 
0.261297766929, 0.261746825255, 0.262194972844, 0.26264221124, 
0.263088541977, 0.263533966582, 0.263978486573, 0.264422103459, 
0.264864818742, 0.265306633916, 0.265747550468, 0.266187569874, 
0.266626693606, 0.267064923125, 0.267502259887, 0.267938705337, 
0.268374260917, 0.268808928057, 0.269242708181, 0.269675602708, 
0.270107613045, 0.270538740596, 0.270968986755, 0.271398352911, 
0.271826840443, 0.272254450724, 0.272681185122, 0.273107044995, 
0.273532031696, 0.27395614657, 0.274379390955, 0.274801766184, 
0.27522327358, 0.275643914463, 0.276063690144, 0.276482601927, 
0.276900651111, 0.277317838987, 0.277734166841, 0.278149635951, 
0.278564247589, 0.278978003022, 0.279390903509, 0.279802950304, 
0.280214144653, 0.280624487797, 0.281033980972, 0.281442625405, 
0.281850422319, 0.282257372931, 0.282663478451, 0.283068740084, 
0.283473159028, 0.283876736476, 0.284279473616, 0.284681371627, 
0.285082431686, 0.285482654962, 0.285882042619, 0.286280595816, 
0.286678315704, 0.287075203432, 0.28747126014, 0.287866486966, 
0.288260885038, 0.288654455484, 0.289047199422, 0.289439117966, 
0.289830212227, 0.290220483307, 0.290609932306, 0.290998560316, 
0.291386368426, 0.291773357718, 0.292159529271, 0.292544884157, 
0.292929423444, 0.293313148194, 0.293696059465, 0.29407815831, 
0.294459445777, 0.294839922907, 0.29521959074, 0.295598450308, 
0.295976502639, 0.296353748757, 0.296730189681, 0.297105826424, 
0.297480659996, 0.297854691402, 0.298227921641, 0.298600351708, 
0.298971982594, 0.299342815286, 0.299712850765, 0.300082090009, 
0.300450533989, 0.300818183674, 0.301185040027, 0.301551104009, 
0.301916376573, 0.302280858671, 0.302644551249, 0.303007455249, 
0.303369571608, 0.30373090126, 0.304091445134, 0.304451204155, 
0.304810179244, 0.305168371318, 0.305525781289, 0.305882410065, 
0.306238258551, 0.306593327647, 0.30694761825, 0.307301131252, 
0.30765386754, 0.308005827999, 0.30835701351, 0.308707424949, 
0.309057063188, 0.309405929096, 0.309754023538, 0.310101347375, 
0.310447901463, 0.310793686656, 0.311138703804, 0.311482953752, 
0.311826437342, 0.312169155414, 0.3125111088, 0.312852298333, 
0.313192724839, 0.313532389143, 0.313871292064, 0.314209434418, 
0.31454681702, 0.314883440677, 0.315219306196, 0.315554414379, 
0.315888766025, 0.31622236193, 0.316555202884, 0.316887289677, 
0.317218623093, 0.317549203914, 0.317879032918, 0.31820811088, 
0.318536438572, 0.318864016761, 0.319190846212, 0.319516927687, 
0.319842261944, 0.320166849739, 0.320490691821, 0.320813788941, 
0.321136141844, 0.32145775127, 0.32177861796, 0.322098742649, 
0.32241812607, 0.322736768951, 0.32305467202, 0.323371835999, 
0.323688261608, 0.324003949565, 0.324318900584, 0.324633115374, 
0.324946594645, 0.325259339102, 0.325571349445, 0.325882626374, 
0.326193170585, 0.32650298277, 0.326812063621, 0.327120413824, 
0.327428034062, 0.327734925019, 0.328041087371, 0.328346521794, 
0.328651228962, 0.328955209544, 0.329258464207, 0.329560993615, 
0.32986279843, 0.33016387931, 0.330464236912, 0.330763871888, 
0.331062784889, 0.331360976562, 0.331658447552, 0.331955198502, 
0.332251230051, 0.332546542836, 0.33284113749, 0.333135014646, 
0.333428174933, 0.333720618976, 0.334012347399, 0.334303360823, 
0.334593659867, 0.334883245146, 0.335172117274, 0.335460276861, 
0.335747724516, 0.336034460843, 0.336320486447, 0.336605801928, 
0.336890407883, 0.337174304908, 0.337457493597, 0.33773997454, 
0.338021748325, 0.338302815538, 0.338583176762, 0.338862832579, 
0.339141783565, 0.339420030298, 0.339697573351, 0.339974413296, 
0.340250550701, 0.340525986133, 0.340800720156, 0.341074753331, 
0.341348086219, 0.341620719376, 0.341892653358, 0.342163888717, 
0.342434426003, 0.342704265764, 0.342973408546, 0.343241854893, 
0.343509605345, 0.343776660442, 0.344043020721, 0.344308686715, 
0.344573658957, 0.344837937978, 0.345101524305, 0.345364418464, 
0.345626620979, 0.34588813237, 0.346148953157, 0.346409083858, 
0.346668524987, 0.346927277056, 0.347185340577, 0.347442716058, 
0.347699404006, 0.347955404925, 0.348210719317, 0.348465347682, 
0.348719290519, 0.348972548324, 0.34922512159, 0.349477010809, 
0.349728216472, 0.349978739066, 0.350228579078, 0.35047773699, 
0.350726213286, 0.350974008444, 0.351221122943, 0.351467557258, 
0.351713311863, 0.351958387231, 0.352202783831, 0.352446502132, 
0.352689542598, 0.352931905695, 0.353173591885, 0.353414601628, 
0.353654935383, 0.353894593605, 0.35413357675, 0.354371885269, 
0.354609519615, 0.354846480236, 0.355082767578, 0.355318382088, 
0.355553324208, 0.355787594379, 0.356021193043, 0.356254120636, 
0.356486377594, 0.356717964351, 0.35694888134, 0.357179128992, 
0.357408707735, 0.357637617995, 0.357865860199, 0.35809343477, 
0.358320342128, 0.358546582694, 0.358772156887, 0.358997065122, 
0.359221307813, 0.359444885374, 0.359667798216, 0.359890046748, 
0.360111631378, 0.360332552511, 0.360552810552, 0.360772405903, 
0.360991338966, 0.361209610138, 0.361427219818, 0.361644168402, 
0.361860456282, 0.362076083852, 0.362291051503, 0.362505359623, 
0.3627190086, 0.362931998819, 0.363144330665, 0.363356004521, 
0.363567020766, 0.36377737978, 0.363987081941, 0.364196127625, 
0.364404517206, 0.364612251057, 0.364819329549, 0.365025753052, 
0.365231521933, 0.365436636559, 0.365641097295, 0.365844904505, 
0.366048058549, 0.366250559788, 0.366452408581, 0.366653605284, 
0.366854150253, 0.367054043843, 0.367253286404, 0.367451878289, 
0.367649819847, 0.367847111425, 0.36804375337, 0.368239746027, 
0.368435089738, 0.368629784846, 0.368823831692, 0.369017230612, 
0.369209981946, 0.369402086029, 0.369593543196, 0.369784353778, 
0.369974518108, 0.370164036516, 0.370352909329, 0.370541136876, 
0.370728719481, 0.37091565747, 0.371101951163, 0.371287600884, 
0.371472606951, 0.371656969683, 0.371840689397, 0.372023766409, 
0.372206201032, 0.37238799358, 0.372569144364, 0.372749653693, 
0.372929521876, 0.373108749221, 0.373287336032, 0.373465282615, 
0.373642589273, 0.373819256306, 0.373995284015, 0.374170672699, 
0.374345422656, 0.374519534181, 0.37469300757, 0.374865843115, 
0.375038041109, 0.375209601842, 0.375380525604, 0.375550812683, 
0.375720463365, 0.375889477937, 0.37605785668, 0.37622559988, 
0.376392707816, 0.376559180769, 0.376725019018, 0.37689022284, 
0.377054792511, 0.377218728306, 0.377382030499, 0.377544699361, 
0.377706735164, 0.377868138178, 0.37802890867, 0.378189046907, 
0.378348553157, 0.378507427682, 0.378665670746, 0.378823282612, 
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0.250714384101, 0.250242982463, 0.249770628616, 0.249297320778, 
0.248823057154, 0.248347835939, 0.24787165532, 0.247394513471, 
0.246916408556, 0.246437338729, 0.245957302131, 0.245476296896, 
0.244994321143, 0.244511372982, 0.244027450511, 0.243542551818, 
0.243056674978, 0.242569818056, 0.242081979103, 0.241593156162, 
0.24110334726, 0.240612550416, 0.240120763634, 0.239627984909, 
0.23913421222, 0.238639443537, 0.238143676816, 0.23764691, 
0.237149141021, 0.236650367797, 0.236150588234, 0.235649800223, 
0.235148001646, 0.234645190367, 0.234141364239, 0.233636521103, 
0.233130658784, 0.232623775093, 0.23211586783, 0.231606934779, 
0.23109697371, 0.230585982379, 0.230073958527, 0.229560899883, 
0.229046804158, 0.228531669051, 0.228015492244, 0.227498271406, 
0.226980004189, 0.22646068823, 0.225940321153, 0.225418900562, 
0.224896424048, 0.224372889187, 0.223848293537, 0.22332263464, 
0.222795910022, 0.222268117192, 0.221739253644, 0.221209316853, 
0.220678304278, 0.220146213361, 0.219613041525, 0.219078786178, 
0.218543444708, 0.218007014486, 0.217469492865, 0.21693087718, 
0.216391164747, 0.215850352864, 0.215308438808, 0.21476541984, 
0.2142212932, 0.213676056109, 0.213129705768, 0.212582239359, 
0.212033654044, 0.211483946962, 0.210933115235, 0.210381155963, 
0.209828066225, 0.209273843078, 0.20871848356, 0.208161984685, 
0.207604343447, 0.207045556815, 0.20648562174, 0.205924535147, 
0.20536229394, 0.204798894998, 0.204234335179, 0.203668611317, 
0.20310172022, 0.202533658675, 0.201964423442, 0.201394011258, 
0.200822418835, 0.200249642858, 0.199675679989, 0.199100526863, 
0.198524180089, 0.197946636249, 0.197367891899, 0.196787943569, 
0.196206787758, 0.195624420943, 0.195040839567, 0.19445604005, 
0.19387001878, 0.193282772116, 0.192694296391, 0.192104587904, 
0.191513642926, 0.190921457698, 0.19032802843, 0.189733351301, 
0.189137422456, 0.188540238012, 0.187941794051, 0.187342086623, 
0.186741111744, 0.186138865399, 0.185535343536, 0.18493054207, 
0.184324456881, 0.183717083814, 0.183108418678, 0.182498457245, 
0.18188719525, 0.181274628394, 0.180660752337, 0.180045562701, 
0.179429055072, 0.178811224993, 0.178192067971, 0.177571579471, 
0.176949754916, 0.176326589689, 0.175702079132, 0.175076218543, 
0.174449003177, 0.173820428247, 0.173190488919, 0.172559180317, 
0.171926497516, 0.171292435549, 0.170656989399, 0.170020154004, 
0.16938192425, 0.168742294978, 0.168101260978, 0.167458816989, 
0.166814957701, 0.166169677749, 0.165522971719, 0.164874834141, 
0.164225259493, 0.163574242196, 0.162921776617, 0.162267857065, 
0.161612477792, 0.160955632992, 0.160297316801, 0.159637523292, 
0.158976246478, 0.158313480311, 0.15764921868, 0.156983455408, 
0.156316184255, 0.155647398914, 0.154977093011, 0.154305260103, 
0.15363189368, 0.152956987158, 0.152280533885, 0.151602527134, 
0.150922960105, 0.15024182592, 0.149559117629, 0.148874828201, 
0.148188950527, 0.147501477416, 0.146812401597, 0.146121715716, 
0.145429412331, 0.144735483917, 0.14403992286, 0.143342721456, 
0.142643871912, 0.14194336634, 0.141241196759, 0.140537355092, 
0.139831833164, 0.139124622701, 0.138415715327, 0.137705102563, 
0.136992775823, 0.136278726418, 0.135562945545, 0.134845424292, 
0.134126153634, 0.133405124429, 0.132682327417, 0.131957753219, 
0.131231392331, 0.130503235127, 0.129773271849, 0.129041492613, 
0.1283078874, 0.127572446055, 0.126835158285, 0.126096013656, 
0.125355001589, 0.124612111359, 0.123867332088, 0.123120652746, 
0.122372062145, 0.121621548938, 0.120869101612, 0.120114708488, 
0.119358357714, 0.118600037264, 0.117839734932, 0.117077438329, 
0.116313134879, 0.115546811812, 0.114778456164, 0.114008054769, 
0.113235594256, 0.112461061041, 0.111684441327, 0.110905721095, 
0.110124886098, 0.109341921858, 0.108556813661, 0.107769546546, 
0.106980105304, 0.106188474468, 0.105394638309, 0.104598580828, 
0.103800285749, 0.10299973651, 0.102196916259, 0.101391807842, 
0.1005843938, 0.0997746563536, 0.0989625774004, 0.0981481385023, 
0.0973313208777, 0.0965121053906, 0.0956904725411, 0.0948664024544, 
0.0940398748697, 0.0932108691291, 0.0923793641651, 0.0915453384885, 
0.0907087701755, 0.0898696368538, 0.0890279156891, 0.0881835833697, 
0.087336616092, 0.0864869895441, 0.0856346788892, 0.0847796587481, 
0.0839219031814, 0.08306138567, 0.0821980790956, 0.0813319557199, 
0.0804629871627, 0.0795911443789, 0.0787163976352, 0.0778387164844, 
0.0769580697397, 0.0760744254467, 0.0751877508543, 0.074298012385, 
0.0734051756019, 0.0725092051756, 0.0716100648488, 0.0707077173982, 
0.069802124596, 0.0688932471675, 0.0679810447477, 0.0670654758347, 
0.0661464977405, 0.0652240665394, 0.0642981370127, 0.0633686625906, 
0.0624355952904, 0.0614988856508, 0.0605584826623, 0.0596143336931, 
0.05866638441, 0.0577145786948, 0.0567588585541, 0.0557991640245, 
0.0548354330697, 0.0538676014717, 0.0528956027139, 0.051919367856, 
0.0509388253991, 0.0499539011423, 0.048964518027, 0.0479705959707, 
0.0469720516867, 0.0459687984913, 0.0449607460939, 0.0439478003716, 
0.0429298631245, 0.0419068318115, 0.0408785992629, 0.0398450533701, 
0.0388060767473, 0.0377615463648, 0.0367113331503, 0.0356553015556, 
0.0345933090853, 0.033525205785, 0.0324508336859, 0.0313700262033, 
0.0302826074868, 0.029188391722, 0.0280871823847, 0.0269787714532, 
0.0258629385876, 0.0247394502967, 0.0236080591234, 0.0224685029043, 
0.0213205041901, 0.0201637699709, 0.0189979919374, 0.0178228476567, 
0.0166380032833, 0.0154431188471, 0.0142378578907, 0.0130219045529, 
0.0117949936695, 0.0105569642697, 0.00930785665637, 0.00804809441177, 
0.00677884150883, 0.00550274714411, 0.00422563087009, 0.00296073311723, 
0.00174111855358};

static const double yu[2001]={
0.0548354330697, 0.0557991640245, 0.0567588585541, 0.0577145786948, 
0.05866638441, 0.0596143336931, 0.0605584826623, 0.0614988856508, 
0.0624355952904, 0.0633686625906, 0.0642981370127, 0.0652240665394, 
0.0661464977405, 0.0670654758347, 0.0679810447477, 0.0688932471675, 
0.069802124596, 0.0707077173982, 0.0716100648488, 0.0725092051756, 
0.0734051756019, 0.074298012385, 0.0751877508543, 0.0760744254467, 
0.0769580697397, 0.0778387164844, 0.0787163976352, 0.0795911443789, 
0.0804629871627, 0.0813319557199, 0.0821980790956, 0.08306138567, 
0.0839219031814, 0.0847796587481, 0.0856346788892, 0.0864869895441, 
0.087336616092, 0.0881835833697, 0.0890279156891, 0.0898696368538, 
0.0907087701755, 0.0915453384885, 0.0923793641651, 0.0932108691291, 
0.0940398748697, 0.0948664024544, 0.0956904725411, 0.0965121053906, 
0.0973313208777, 0.0981481385023, 0.0989625774004, 0.0997746563536, 
0.1005843938, 0.101391807842, 0.102196916259, 0.10299973651, 
0.103800285749, 0.104598580828, 0.105394638309, 0.106188474468, 
0.106980105304, 0.107769546546, 0.108556813661, 0.109341921858, 
0.110124886098, 0.110905721095, 0.111684441327, 0.112461061041, 
0.113235594256, 0.114008054769, 0.114778456164, 0.115546811812, 
0.116313134879, 0.117077438329, 0.117839734932, 0.118600037264, 
0.119358357714, 0.120114708488, 0.120869101612, 0.121621548938, 
0.122372062145, 0.123120652746, 0.123867332088, 0.124612111359, 
0.125355001589, 0.126096013656, 0.126835158285, 0.127572446055, 
0.1283078874, 0.129041492613, 0.129773271849, 0.130503235127, 
0.131231392331, 0.131957753219, 0.132682327417, 0.133405124429, 
0.134126153634, 0.134845424292, 0.135562945545, 0.136278726418, 
0.136992775823, 0.137705102563, 0.138415715327, 0.139124622701, 
0.139831833164, 0.140537355092, 0.141241196759, 0.14194336634, 
0.142643871912, 0.143342721456, 0.14403992286, 0.144735483917, 
0.145429412331, 0.146121715716, 0.146812401597, 0.147501477416, 
0.148188950527, 0.148874828201, 0.149559117629, 0.15024182592, 
0.150922960105, 0.151602527134, 0.152280533885, 0.152956987158, 
0.15363189368, 0.154305260103, 0.154977093011, 0.155647398914, 
0.156316184255, 0.156983455408, 0.15764921868, 0.158313480311, 
0.158976246478, 0.159637523292, 0.160297316801, 0.160955632992, 
0.161612477792, 0.162267857065, 0.162921776617, 0.163574242196, 
0.164225259493, 0.164874834141, 0.165522971719, 0.166169677749, 
0.166814957701, 0.167458816989, 0.168101260978, 0.168742294978, 
0.16938192425, 0.170020154004, 0.170656989399, 0.171292435549, 
0.171926497516, 0.172559180317, 0.173190488919, 0.173820428247, 
0.174449003177, 0.175076218543, 0.175702079132, 0.176326589689, 
0.176949754916, 0.177571579471, 0.178192067971, 0.178811224993, 
0.179429055072, 0.180045562701, 0.180660752337, 0.181274628394, 
0.18188719525, 0.182498457245, 0.183108418678, 0.183717083814, 
0.184324456881, 0.18493054207, 0.185535343536, 0.186138865399, 
0.186741111744, 0.187342086623, 0.187941794051, 0.188540238012, 
0.189137422456, 0.189733351301, 0.19032802843, 0.190921457698, 
0.191513642926, 0.192104587904, 0.192694296391, 0.193282772116, 
0.19387001878, 0.19445604005, 0.195040839567, 0.195624420943, 
0.196206787758, 0.196787943569, 0.197367891899, 0.197946636249, 
0.198524180089, 0.199100526863, 0.199675679989, 0.200249642858, 
0.200822418835, 0.201394011258, 0.201964423442, 0.202533658675, 
0.20310172022, 0.203668611317, 0.204234335179, 0.204798894998, 
0.20536229394, 0.205924535147, 0.20648562174, 0.207045556815, 
0.207604343447, 0.208161984685, 0.20871848356, 0.209273843078, 
0.209828066225, 0.210381155963, 0.210933115235, 0.211483946962, 
0.212033654044, 0.212582239359, 0.213129705768, 0.213676056109, 
0.2142212932, 0.21476541984, 0.215308438808, 0.215850352864, 
0.216391164747, 0.21693087718, 0.217469492865, 0.218007014486, 
0.218543444708, 0.219078786178, 0.219613041525, 0.220146213361, 
0.220678304278, 0.221209316853, 0.221739253644, 0.222268117192, 
0.222795910022, 0.22332263464, 0.223848293537, 0.224372889187, 
0.224896424048, 0.225418900562, 0.225940321153, 0.22646068823, 
0.226980004189, 0.227498271406, 0.228015492244, 0.228531669051, 
0.229046804158, 0.229560899883, 0.230073958527, 0.230585982379, 
0.23109697371, 0.231606934779, 0.23211586783, 0.232623775093, 
0.233130658784, 0.233636521103, 0.234141364239, 0.234645190367, 
0.235148001646, 0.235649800223, 0.236150588234, 0.236650367797, 
0.237149141021, 0.23764691, 0.238143676816, 0.238639443537, 
0.23913421222, 0.239627984909, 0.240120763634, 0.240612550416, 
0.24110334726, 0.241593156162, 0.242081979103, 0.242569818056, 
0.243056674978, 0.243542551818, 0.244027450511, 0.244511372982, 
0.244994321143, 0.245476296896, 0.245957302131, 0.246437338729, 
0.246916408556, 0.247394513471, 0.24787165532, 0.248347835939, 
0.248823057154, 0.249297320778, 0.249770628616, 0.250242982463, 
0.250714384101, 0.251184835304, 0.251654337834, 0.252122893446, 
0.252590503882, 0.253057170876, 0.253522896151, 0.253987681421, 
0.254451528389, 0.254914438751, 0.255376414192, 0.255837456386, 
0.256297567001, 0.256756747694, 0.257215000112, 0.257672325893, 
0.258128726668, 0.258584204057, 0.259038759672, 0.259492395116, 
0.259945111982, 0.260396911857, 0.260847796317, 0.261297766929, 
0.261746825255, 0.262194972844, 0.26264221124, 0.263088541977, 
0.263533966582, 0.263978486573, 0.264422103459, 0.264864818742, 
0.265306633916, 0.265747550468, 0.266187569874, 0.266626693606, 
0.267064923125, 0.267502259887, 0.267938705337, 0.268374260917, 
0.268808928057, 0.269242708181, 0.269675602708, 0.270107613045, 
0.270538740596, 0.270968986755, 0.271398352911, 0.271826840443, 
0.272254450724, 0.272681185122, 0.273107044995, 0.273532031696, 
0.27395614657, 0.274379390955, 0.274801766184, 0.27522327358, 
0.275643914463, 0.276063690144, 0.276482601927, 0.276900651111, 
0.277317838987, 0.277734166841, 0.278149635951, 0.278564247589, 
0.278978003022, 0.279390903509, 0.279802950304, 0.280214144653, 
0.280624487797, 0.281033980972, 0.281442625405, 0.281850422319, 
0.282257372931, 0.282663478451, 0.283068740084, 0.283473159028, 
0.283876736476, 0.284279473616, 0.284681371627, 0.285082431686, 
0.285482654962, 0.285882042619, 0.286280595816, 0.286678315704, 
0.287075203432, 0.28747126014, 0.287866486966, 0.288260885038, 
0.288654455484, 0.289047199422, 0.289439117966, 0.289830212227, 
0.290220483307, 0.290609932306, 0.290998560316, 0.291386368426, 
0.291773357718, 0.292159529271, 0.292544884157, 0.292929423444, 
0.293313148194, 0.293696059465, 0.29407815831, 0.294459445777, 
0.294839922907, 0.29521959074, 0.295598450308, 0.295976502639, 
0.296353748757, 0.296730189681, 0.297105826424, 0.297480659996, 
0.297854691402, 0.298227921641, 0.298600351708, 0.298971982594, 
0.299342815286, 0.299712850765, 0.300082090009, 0.300450533989, 
0.300818183674, 0.301185040027, 0.301551104009, 0.301916376573, 
0.302280858671, 0.302644551249, 0.303007455249, 0.303369571608, 
0.30373090126, 0.304091445134, 0.304451204155, 0.304810179244, 
0.305168371318, 0.305525781289, 0.305882410065, 0.306238258551, 
0.306593327647, 0.30694761825, 0.307301131252, 0.30765386754, 
0.308005827999, 0.30835701351, 0.308707424949, 0.309057063188, 
0.309405929096, 0.309754023538, 0.310101347375, 0.310447901463, 
0.310793686656, 0.311138703804, 0.311482953752, 0.311826437342, 
0.312169155414, 0.3125111088, 0.312852298333, 0.313192724839, 
0.313532389143, 0.313871292064, 0.314209434418, 0.31454681702, 
0.314883440677, 0.315219306196, 0.315554414379, 0.315888766025, 
0.31622236193, 0.316555202884, 0.316887289677, 0.317218623093, 
0.317549203914, 0.317879032918, 0.31820811088, 0.318536438572, 
0.318864016761, 0.319190846212, 0.319516927687, 0.319842261944, 
0.320166849739, 0.320490691821, 0.320813788941, 0.321136141844, 
0.32145775127, 0.32177861796, 0.322098742649, 0.32241812607, 
0.322736768951, 0.32305467202, 0.323371835999, 0.323688261608, 
0.324003949565, 0.324318900584, 0.324633115374, 0.324946594645, 
0.325259339102, 0.325571349445, 0.325882626374, 0.326193170585, 
0.32650298277, 0.326812063621, 0.327120413824, 0.327428034062, 
0.327734925019, 0.328041087371, 0.328346521794, 0.328651228962, 
0.328955209544, 0.329258464207, 0.329560993615, 0.32986279843, 
0.33016387931, 0.330464236912, 0.330763871888, 0.331062784889, 
0.331360976562, 0.331658447552, 0.331955198502, 0.332251230051, 
0.332546542836, 0.33284113749, 0.333135014646, 0.333428174933, 
0.333720618976, 0.334012347399, 0.334303360823, 0.334593659867, 
0.334883245146, 0.335172117274, 0.335460276861, 0.335747724516, 
0.336034460843, 0.336320486447, 0.336605801928, 0.336890407883, 
0.337174304908, 0.337457493597, 0.33773997454, 0.338021748325, 
0.338302815538, 0.338583176762, 0.338862832579, 0.339141783565, 
0.339420030298, 0.339697573351, 0.339974413296, 0.340250550701, 
0.340525986133, 0.340800720156, 0.341074753331, 0.341348086219, 
0.341620719376, 0.341892653358, 0.342163888717, 0.342434426003, 
0.342704265764, 0.342973408546, 0.343241854893, 0.343509605345, 
0.343776660442, 0.344043020721, 0.344308686715, 0.344573658957, 
0.344837937978, 0.345101524305, 0.345364418464, 0.345626620979, 
0.34588813237, 0.346148953157, 0.346409083858, 0.346668524987, 
0.346927277056, 0.347185340577, 0.347442716058, 0.347699404006, 
0.347955404925, 0.348210719317, 0.348465347682, 0.348719290519, 
0.348972548324, 0.34922512159, 0.349477010809, 0.349728216472, 
0.349978739066, 0.350228579078, 0.35047773699, 0.350726213286, 
0.350974008444, 0.351221122943, 0.351467557258, 0.351713311863, 
0.351958387231, 0.352202783831, 0.352446502132, 0.352689542598, 
0.352931905695, 0.353173591885, 0.353414601628, 0.353654935383, 
0.353894593605, 0.35413357675, 0.354371885269, 0.354609519615, 
0.354846480236, 0.355082767578, 0.355318382088, 0.355553324208, 
0.355787594379, 0.356021193043, 0.356254120636, 0.356486377594, 
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0.299712850765, 0.299342815286, 0.298971982594, 0.298600351708, 
0.298227921641, 0.297854691402, 0.297480659996, 0.297105826424, 
0.296730189681, 0.296353748757, 0.295976502639, 0.295598450308, 
0.29521959074, 0.294839922907, 0.294459445777, 0.29407815831, 
0.293696059465, 0.293313148194, 0.292929423444, 0.292544884157, 
0.292159529271, 0.291773357718, 0.291386368426, 0.290998560316, 
0.290609932306, 0.290220483307, 0.289830212227, 0.289439117966, 
0.289047199422, 0.288654455484, 0.288260885038, 0.287866486966, 
0.28747126014, 0.287075203432, 0.286678315704, 0.286280595816, 
0.285882042619, 0.285482654962, 0.285082431686, 0.284681371627, 
0.284279473616, 0.283876736476, 0.283473159028, 0.283068740084, 
0.282663478451, 0.282257372931, 0.281850422319, 0.281442625405, 
0.281033980972, 0.280624487797, 0.280214144653, 0.279802950304, 
0.279390903509, 0.278978003022, 0.278564247589, 0.278149635951, 
0.277734166841, 0.277317838987, 0.276900651111, 0.276482601927, 
0.276063690144, 0.275643914463, 0.27522327358, 0.274801766184, 
0.274379390955, 0.27395614657, 0.273532031696, 0.273107044995, 
0.272681185122, 0.272254450724, 0.271826840443, 0.271398352911, 
0.270968986755, 0.270538740596, 0.270107613045, 0.269675602708, 
0.269242708181, 0.268808928057, 0.268374260917, 0.267938705337, 
0.267502259887, 0.267064923125, 0.266626693606, 0.266187569874, 
0.265747550468, 0.265306633916, 0.264864818742, 0.264422103459, 
0.263978486573, 0.263533966582, 0.263088541977, 0.26264221124, 
0.262194972844, 0.261746825255, 0.261297766929, 0.260847796317, 
0.260396911857, 0.259945111982, 0.259492395116, 0.259038759672, 
0.258584204057, 0.258128726668, 0.257672325893, 0.257215000112, 
0.256756747694, 0.256297567001, 0.255837456386, 0.255376414192, 
0.254914438751, 0.254451528389, 0.253987681421, 0.253522896151, 
0.253057170876, 0.252590503882, 0.252122893446, 0.251654337834, 
0.251184835304, 0.250714384101, 0.250242982463, 0.249770628616, 
0.249297320778, 0.248823057154, 0.248347835939, 0.24787165532, 
0.247394513471, 0.246916408556, 0.246437338729, 0.245957302131, 
0.245476296896, 0.244994321143, 0.244511372982, 0.244027450511, 
0.243542551818, 0.243056674978, 0.242569818056, 0.242081979103, 
0.241593156162, 0.24110334726, 0.240612550416, 0.240120763634, 
0.239627984909, 0.23913421222, 0.238639443537, 0.238143676816, 
0.23764691, 0.237149141021, 0.236650367797, 0.236150588234, 
0.235649800223, 0.235148001646, 0.234645190367, 0.234141364239, 
0.233636521103, 0.233130658784, 0.232623775093, 0.23211586783, 
0.231606934779, 0.23109697371, 0.230585982379, 0.230073958527, 
0.229560899883, 0.229046804158, 0.228531669051, 0.228015492244, 
0.227498271406, 0.226980004189, 0.22646068823, 0.225940321153, 
0.225418900562, 0.224896424048, 0.224372889187, 0.223848293537, 
0.22332263464, 0.222795910022, 0.222268117192, 0.221739253644, 
0.221209316853, 0.220678304278, 0.220146213361, 0.219613041525, 
0.219078786178, 0.218543444708, 0.218007014486, 0.217469492865, 
0.21693087718, 0.216391164747, 0.215850352864, 0.215308438808, 
0.21476541984, 0.2142212932, 0.213676056109, 0.213129705768, 
0.212582239359, 0.212033654044, 0.211483946962, 0.210933115235, 
0.210381155963, 0.209828066225, 0.209273843078, 0.20871848356, 
0.208161984685, 0.207604343447, 0.207045556815, 0.20648562174, 
0.205924535147, 0.20536229394, 0.204798894998, 0.204234335179, 
0.203668611317, 0.20310172022, 0.202533658675, 0.201964423442, 
0.201394011258, 0.200822418835, 0.200249642858, 0.199675679989, 
0.199100526863, 0.198524180089, 0.197946636249, 0.197367891899, 
0.196787943569, 0.196206787758, 0.195624420943, 0.195040839567, 
0.19445604005, 0.19387001878, 0.193282772116, 0.192694296391, 
0.192104587904, 0.191513642926, 0.190921457698, 0.19032802843, 
0.189733351301, 0.189137422456, 0.188540238012, 0.187941794051, 
0.187342086623, 0.186741111744, 0.186138865399, 0.185535343536, 
0.18493054207, 0.184324456881, 0.183717083814, 0.183108418678, 
0.182498457245, 0.18188719525, 0.181274628394, 0.180660752337, 
0.180045562701, 0.179429055072, 0.178811224993, 0.178192067971, 
0.177571579471, 0.176949754916, 0.176326589689, 0.175702079132, 
0.175076218543, 0.174449003177, 0.173820428247, 0.173190488919, 
0.172559180317, 0.171926497516, 0.171292435549, 0.170656989399, 
0.170020154004, 0.16938192425, 0.168742294978, 0.168101260978, 
0.167458816989, 0.166814957701, 0.166169677749, 0.165522971719, 
0.164874834141, 0.164225259493, 0.163574242196, 0.162921776617, 
0.162267857065, 0.161612477792, 0.160955632992, 0.160297316801, 
0.159637523292, 0.158976246478, 0.158313480311, 0.15764921868, 
0.156983455408, 0.156316184255, 0.155647398914, 0.154977093011, 
0.154305260103, 0.15363189368, 0.152956987158, 0.152280533885, 
0.151602527134, 0.150922960105, 0.15024182592, 0.149559117629, 
0.148874828201, 0.148188950527, 0.147501477416, 0.146812401597, 
0.146121715716, 0.145429412331, 0.144735483917, 0.14403992286, 
0.143342721456, 0.142643871912, 0.14194336634, 0.141241196759, 
0.140537355092, 0.139831833164, 0.139124622701, 0.138415715327, 
0.137705102563, 0.136992775823, 0.136278726418, 0.135562945545, 
0.134845424292, 0.134126153634, 0.133405124429, 0.132682327417, 
0.131957753219, 0.131231392331, 0.130503235127, 0.129773271849, 
0.129041492613, 0.1283078874, 0.127572446055, 0.126835158285, 
0.126096013656, 0.125355001589, 0.124612111359, 0.123867332088, 
0.123120652746, 0.122372062145, 0.121621548938, 0.120869101612, 
0.120114708488, 0.119358357714, 0.118600037264, 0.117839734932, 
0.117077438329, 0.116313134879, 0.115546811812, 0.114778456164, 
0.114008054769, 0.113235594256, 0.112461061041, 0.111684441327, 
0.110905721095, 0.110124886098, 0.109341921858, 0.108556813661, 
0.107769546546, 0.106980105304, 0.106188474468, 0.105394638309, 
0.104598580828, 0.103800285749, 0.10299973651, 0.102196916259, 
0.101391807842, 0.1005843938, 0.0997746563536, 0.0989625774004, 
0.0981481385023, 0.0973313208777, 0.0965121053906, 0.0956904725411, 
0.0948664024544, 0.0940398748697, 0.0932108691291, 0.0923793641651, 
0.0915453384885, 0.0907087701755, 0.0898696368538, 0.0890279156891, 
0.0881835833697, 0.087336616092, 0.0864869895441, 0.0856346788892, 
0.0847796587481, 0.0839219031814, 0.08306138567, 0.0821980790956, 
0.0813319557199, 0.0804629871627, 0.0795911443789, 0.0787163976352, 
0.0778387164844, 0.0769580697397, 0.0760744254467, 0.0751877508543, 
0.074298012385, 0.0734051756019, 0.0725092051756, 0.0716100648488, 
0.0707077173982, 0.069802124596, 0.0688932471675, 0.0679810447477, 
0.0670654758347, 0.0661464977405, 0.0652240665394, 0.0642981370127, 
0.0633686625906, 0.0624355952904, 0.0614988856508, 0.0605584826623, 
0.0596143336931, 0.05866638441, 0.0577145786948, 0.0567588585541, 
0.0557991640245, 0.0548354330697, 0.0538676014717, 0.0528956027139, 
0.051919367856, 0.0509388253991, 0.0499539011423, 0.048964518027, 
0.0479705959707, 0.0469720516867, 0.0459687984913, 0.0449607460939, 
0.0439478003716, 0.0429298631245, 0.0419068318115, 0.0408785992629, 
0.0398450533701, 0.0388060767473, 0.0377615463648, 0.0367113331503, 
0.0356553015556, 0.0345933090853, 0.033525205785, 0.0324508336859, 
0.0313700262033, 0.0302826074868, 0.029188391722, 0.0280871823847, 
0.0269787714532, 0.0258629385876, 0.0247394502967, 0.0236080591234, 
0.0224685029043, 0.0213205041901, 0.0201637699709, 0.0189979919374, 
0.0178228476567, 0.0166380032833, 0.0154431188471, 0.0142378578907, 
0.0130219045529, 0.0117949936695, 0.0105569642697, 0.00930785665637, 
0.00804809441177, 0.00677884150883, 0.00550274714411, 0.00422563087009, 
0.00296073311723};

static const double d[2001]={
0.00891846716958, 0.00876443255219, 0.00861624109468, 0.00847356111093, 
0.00833608572404, 0.00820353058174, 0.00807563182005, 0.00795214424435, 
0.00783283970125, 0.00771750561822, 0.00760594369111, 0.00749796870249, 
0.00739340745567, 0.0072920978115, 0.00719388781647, 0.00709863491225, 
0.00700620521785, 0.00691647287675, 0.00682931946221, 0.00674463343484, 
0.00666230964713, 0.00658224889015, 0.00650435747851, 0.0064285468696, 
0.00635473331407, 0.00628283753445, 0.00621278442934, 0.00614450280088, 
0.00607792510329, 0.00601298721066, 0.00594962820229, 0.00588779016407, 
0.00582741800439, 0.00576845928355, 0.00571086405537, 0.00565458472007, 
0.00559957588746, 0.00554579424961, 0.00549319846226, 0.00544174903429, 
0.00539140822453, 0.00534213994547, 0.00529390967324, 0.00524668436343, 
0.00520043237232, 0.00515512338308, 0.00511072833663, 0.00506721936676, 
0.00502456973923, 0.00498275379466, 0.00494174689472, 0.00490152537162, 
0.00486206648056, 0.00482334835495, 0.00478534996422, 0.00474805107405, 
0.00471143220883, 0.00467547461629, 0.00464016023403, 0.00460547165794, 
0.00457139211233, 0.00453790542166, 0.00450499598384, 0.00447264874487, 
0.00444084917489, 0.00440958324543, 0.00437883740787, 0.00434859857299, 
0.00431885409155, 0.00428959173587, 0.00426079968232, 0.00423246649468, 
0.00420458110833, 0.00417713281517, 0.00415011124934, 0.00412350637355, 
0.0040973084661, 0.00407150810852, 0.00404609617378, 0.00402106381502, 
0.00399640245485, 0.00397210377509, 0.003948159707, 0.00392456242198, 
0.00390130432261, 0.00387837803418, 0.0038557763965, 0.00383349245613, 
0.00381151945895, 0.003789850843, 0.00376848023166, 0.00374740142715, 
0.00372660840423, 0.00370609530423, 0.00368585642927, 0.00366588623678, 
0.00364617933423, 0.00362673047401, 0.00360753454859, 0.00358858658586, 
0.00356988174466, 0.0035514153104, 0.00353318269104, 0.003515179413, 
0.00349740111743, 0.00347984355648, 0.00346250258978, 0.00344537418107, 
0.0034284543949, 0.00341173939349, 0.0033952254337, 0.00337890886413, 
0.00336278612231, 0.00334685373195, 0.00333110830039, 0.00331554651607, 
0.00330016514607, 0.00328496103385, 0.00326993109691, 0.00325507232467, 
0.00324038177639, 0.00322585657908, 0.00321149392561, 0.00319729107278, 
0.00318324533954, 0.0031693541052, 0.00315561480772, 0.00314202494211, 
0.00312858205881, 0.00311528376217, 0.00310212770895, 0.00308911160692, 
0.00307623321343, 0.00306349033409, 0.00305088082148, 0.00303840257386, 
0.00302605353401, 0.00301383168798, 0.00300173506401, 0.0029897617314, 
0.00297790979945, 0.00296617741639, 0.00295456276843, 0.00294306407875, 
0.00293167960657, 0.00292040764622, 0.00290924652627, 0.00289819460868, 
0.00288725028794, 0.00287641199026, 0.00286567817282, 0.00285504732298, 
0.00284451795754, 0.00283408862203, 0.00282375789002, 0.00281352436244, 
0.0028033866669, 0.00279334345711, 0.00278339341218, 0.00277353523609, 
0.00276376765707, 0.00275408942703, 0.00274449932104, 0.00273499613673, 
0.00272557869385, 0.00271624583369, 0.00270699641862, 0.00269782933163, 
0.0026887434758, 0.00267973777393, 0.00267081116801, 0.00266196261887, 
0.00265319110571, 0.00264449562569, 0.00263587519359, 0.00262732884136, 
0.00261885561778, 0.00261045458806, 0.00260212483355, 0.00259386545131, 
0.00258567555384, 0.00257755426871, 0.00256950073825, 0.00256151411925, 
0.00255359358263, 0.00254573831317, 0.0025379475092, 0.00253022038233, 
0.00252255615716, 0.00251495407104, 0.00250741337376, 0.00249993332737, 
0.00249251320583, 0.00248515229487, 0.00247784989167, 0.00247060530468, 
0.00246341785339, 0.00245628686808, 0.00244921168961, 0.00244219166926, 
0.00243522616847, 0.00242831455864, 0.00242145622099, 0.00241465054629, 
0.00240789693476, 0.0024011947958, 0.00239454354789, 0.00238794261838, 
0.00238139144329, 0.00237488946721, 0.00236843614311, 0.00236203093215, 
0.00235567330357, 0.00234936273451, 0.0023430987099, 0.00233688072225, 
0.00233070827159, 0.00232458086525, 0.0023184980178, 0.00231245925087, 
0.00230646409301, 0.00230051207963, 0.00229460275281, 0.0022887356612, 
0.00228291035992, 0.00227712641041, 0.00227138338037, 0.00226568084357, 
0.00226001837983, 0.00225439557484, 0.00224881202011, 0.00224326731282, 
0.00223776105577, 0.00223229285726, 0.00222686233097, 0.0022214690959, 
0.00221611277629, 0.00221079300148, 0.00220550940586, 0.00220026162879, 
0.00219504931448, 0.00218987211194, 0.00218472967488, 0.00217962166166, 
0.00217454773517, 0.00216950756278, 0.00216450081626, 0.00215952717173, 
0.00215458630953, 0.00214967791421, 0.00214480167443, 0.00213995728291, 
0.00213514443635, 0.00213036283536, 0.00212561218441, 0.00212089219178, 
0.00211620256947, 0.00211154303315, 0.00210691330211, 0.00210231309919, 
0.00209774215075, 0.00209320018657, 0.00208868693983, 0.00208420214707, 
0.00207974554808, 0.0020753168859, 0.00207091590675, 0.00206654236, 
0.00206219599808, 0.00205787657648, 0.00205358385367, 0.00204931759106, 
0.00204507755298, 0.0020408635066, 0.00203667522192, 0.00203251247167, 
0.00202837503137, 0.00202426267917, 0.00202017519591, 0.00201611236501, 
0.00201207397248, 0.00200805980684, 0.00200406965912, 0.00200010332279, 
0.00199616059376, 0.00199224127032, 0.0019883451531, 0.00198447204504, 
0.00198062175139, 0.00197679407963, 0.00197298883945, 0.00196920584273, 
0.00196544490352, 0.00196170583797, 0.00195798846434, 0.00195429260293, 
0.00195061807608, 0.00194696470816, 0.00194333232548, 0.00193972075632, 
0.00193612983087, 0.00193255938122, 0.00192900924132, 0.00192547924697, 
0.00192196923578, 0.00191847904716, 0.00191500852226, 0.00191155750401, 
0.00190812583702, 0.00190471336763, 0.00190131994382, 0.00189794541523, 
0.00189458963314, 0.00189125245041, 0.0018879337215, 0.00188463330243, 
0.00188135105074, 0.00187808682551, 0.00187484048732, 0.00187161189821, 
0.00186840092171, 0.00186520742277, 0.00186203126776, 0.00185887232445, 
0.00185573046201, 0.00185260555097, 0.0018494974632, 0.00184640607191, 
0.00184333125163, 0.00184027287815, 0.00183723082859, 0.00183420498131, 
0.0018311952159, 0.00182820141321, 0.00182522345529, 0.00182226122539, 
0.00181931460795, 0.00181638348858, 0.00181346775404, 0.00181056729223, 
0.00180768199218, 0.00180481174402, 0.001801956439, 0.00179911596944, 
0.00179629022872, 0.0017934791113, 0.00179068251268, 0.00178790032937, 
0.00178513245892, 0.00178237879988, 0.00177963925179, 0.00177691371518, 
0.00177420209154, 0.00177150428333, 0.00176882019394, 0.00176614972771, 
0.00176349278989, 0.00176084928666, 0.00175821912508, 0.00175560221311, 
0.00175299845961, 0.00175040777426, 0.00174783006766, 0.00174526525121, 
0.00174271323718, 0.00174017393865, 0.00173764726952, 0.00173513314452, 
0.00173263147915, 0.00173014218972, 0.00172766519333, 0.00172520040782, 
0.00172274775183, 0.00172030714473, 0.00171787850665, 0.00171546175844, 
0.00171305682171, 0.00171066361875, 0.00170828207259, 0.00170591210696, 
0.00170355364628, 0.00170120661566, 0.00169887094089, 0.00169654654844, 
0.00169423336543, 0.00169193131966, 0.00168964033956, 0.0016873603542, 
0.00168509129331, 0.00168283308723, 0.00168058566692, 0.00167834896397, 
0.00167612291056, 0.00167390743948, 0.00167170248412, 0.00166950797845, 
0.00166732385702, 0.00166515005497, 0.00166298650798, 0.00166083315233, 
0.00165868992482, 0.00165655676283, 0.00165443360428, 0.0016523203876, 
0.00165021705179, 0.00164812353636, 0.00164603978134, 0.00164396572728, 
0.00164190131523, 0.00163984648678, 0.00163780118397, 0.00163576534937, 
0.00163373892603, 0.00163172185748, 0.00162971408773, 0.00162771556126, 
0.00162572622303, 0.00162374601845, 0.00162177489341, 0.00161981279423, 
0.0016178596677, 0.00161591546103, 0.00161398012191, 0.00161205359842, 
0.0016101358391, 0.00160822679292, 0.00160632640925, 0.00160443463789, 
0.00160255142907, 0.0016006767334, 0.00159881050191, 0.00159695268604, 
0.00159510323762, 0.00159326210886, 0.00159142925237, 0.00158960462117, 
0.00158778816861, 0.00158597984847, 0.00158417961486, 0.0015823874223, 
0.00158060322564, 0.00157882698012, 0.00157705864132, 0.00157529816519, 
0.00157354550803, 0.00157180062648, 0.00157006347754, 0.00156833401853, 
0.00156661220713, 0.00156489800135, 0.00156319135953, 0.00156149224032, 
0.00155980060273, 0.00155811640608, 0.00155643960999, 0.00155477017442, 
0.00155310805964, 0.00155145322621, 0.00154980563502, 0.00154816524726, 
0.00154653202442, 0.00154490592827, 0.00154328692091, 0.00154167496471, 
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0.00139242197469, 0.00139340235401, 0.00139438682093, 0.00139537539178, 
0.00139636808295, 0.00139736491098, 0.00139836589251, 0.00139937104426, 
0.0014003803831, 0.001401393926, 0.00140241169003, 0.00140343369237, 
0.00140445995035, 0.00140549048136, 0.00140652530297, 0.00140756443281, 
0.00140860788865, 0.0014096556884, 0.00141070785004, 0.00141176439173, 
0.0014128253317, 0.00141389068833, 0.00141496048012, 0.00141603472569, 
0.00141711344378, 0.00141819665327, 0.00141928437316, 0.00142037662258, 
0.00142147342079, 0.00142257478717, 0.00142368074124, 0.00142479130266, 
0.00142590649122, 0.00142702632683, 0.00142815082955, 0.00142928001957, 
0.00143041391723, 0.00143155254299, 0.00143269591747, 0.00143384406141, 
0.00143499699572, 0.00143615474142, 0.0014373173197, 0.0014384847519, 
0.00143965705947, 0.00144083426406, 0.00144201638743, 0.0014432034515, 
0.00144439547835, 0.00144559249022, 0.00144679450948, 0.00144800155868, 
0.00144921366051, 0.00145043083783, 0.00145165311365, 0.00145288051115, 
0.00145411305368, 0.00145535076472, 0.00145659366796, 0.00145784178722, 
0.00145909514651, 0.00146035377001, 0.00146161768204, 0.00146288690714, 
0.00146416146999, 0.00146544139545, 0.00146672670856, 0.00146801743456, 
0.00146931359882, 0.00147061522694, 0.00147192234469, 0.001473234978, 
0.00147455315301, 0.00147587689605, 0.00147720623363, 0.00147854119245, 
0.00147988179941, 0.00148122808159, 0.00148258006629, 0.00148393778098, 
0.00148530125335, 0.00148667051128, 0.00148804558287, 0.0014894264964, 
0.00149081328038, 0.00149220596351, 0.0014936045747, 0.0014950091431, 
0.00149641969805, 0.0014978362691, 0.00149925888603, 0.00150068757885, 
0.00150212237777, 0.00150356331324, 0.00150501041593, 0.00150646371673, 
0.00150792324678, 0.00150938903744, 0.0015108611203, 0.00151233952719, 
0.00151382429019, 0.00151531544159, 0.00151681301397, 0.00151831704011, 
0.00151982755306, 0.00152134458612, 0.00152286817284, 0.00152439834701, 
0.00152593514271, 0.00152747859424, 0.00152902873619, 0.0015305856034, 
0.00153214923099, 0.00153371965432, 0.00153529690906, 0.00153688103112, 
0.00153847205672, 0.00154007002233, 0.00154167496471, 0.00154328692091, 
0.00154490592827, 0.00154653202442, 0.00154816524726, 0.00154980563502, 
0.00155145322621, 0.00155310805964, 0.00155477017442, 0.00155643960999, 
0.00155811640608, 0.00155980060273, 0.00156149224032, 0.00156319135953, 
0.00156489800135, 0.00156661220713, 0.00156833401853, 0.00157006347754, 
0.00157180062648, 0.00157354550803, 0.00157529816519, 0.00157705864132, 
0.00157882698012, 0.00158060322564, 0.0015823874223, 0.00158417961486, 
0.00158597984847, 0.00158778816861, 0.00158960462117, 0.00159142925237, 
0.00159326210886, 0.00159510323762, 0.00159695268604, 0.00159881050191, 
0.0016006767334, 0.00160255142907, 0.00160443463789, 0.00160632640925, 
0.00160822679292, 0.0016101358391, 0.00161205359842, 0.00161398012191, 
0.00161591546103, 0.0016178596677, 0.00161981279423, 0.00162177489341, 
0.00162374601845, 0.00162572622303, 0.00162771556126, 0.00162971408773, 
0.00163172185748, 0.00163373892603, 0.00163576534937, 0.00163780118397, 
0.00163984648678, 0.00164190131523, 0.00164396572728, 0.00164603978134, 
0.00164812353636, 0.00165021705179, 0.0016523203876, 0.00165443360428, 
0.00165655676283, 0.00165868992482, 0.00166083315233, 0.00166298650798, 
0.00166515005497, 0.00166732385702, 0.00166950797845, 0.00167170248412, 
0.00167390743948, 0.00167612291056, 0.00167834896397, 0.00168058566692, 
0.00168283308723, 0.00168509129331, 0.0016873603542, 0.00168964033956, 
0.00169193131966, 0.00169423336543, 0.00169654654844, 0.00169887094089, 
0.00170120661566, 0.00170355364628, 0.00170591210696, 0.00170828207259, 
0.00171066361875, 0.00171305682171, 0.00171546175844, 0.00171787850665, 
0.00172030714473, 0.00172274775183, 0.00172520040782, 0.00172766519333, 
0.00173014218972, 0.00173263147915, 0.00173513314452, 0.00173764726952, 
0.00174017393865, 0.00174271323718, 0.00174526525121, 0.00174783006766, 
0.00175040777426, 0.00175299845961, 0.00175560221311, 0.00175821912508, 
0.00176084928666, 0.00176349278989, 0.00176614972771, 0.00176882019394, 
0.00177150428333, 0.00177420209154, 0.00177691371518, 0.00177963925179, 
0.00178237879988, 0.00178513245892, 0.00178790032937, 0.00179068251268, 
0.0017934791113, 0.00179629022872, 0.00179911596944, 0.001801956439, 
0.00180481174402, 0.00180768199218, 0.00181056729223, 0.00181346775404, 
0.00181638348858, 0.00181931460795, 0.00182226122539, 0.00182522345529, 
0.00182820141321, 0.0018311952159, 0.00183420498131, 0.00183723082859, 
0.00184027287815, 0.00184333125163, 0.00184640607191, 0.0018494974632, 
0.00185260555097, 0.00185573046201, 0.00185887232445, 0.00186203126776, 
0.00186520742277, 0.00186840092171, 0.00187161189821, 0.00187484048732, 
0.00187808682551, 0.00188135105074, 0.00188463330243, 0.0018879337215, 
0.00189125245041, 0.00189458963314, 0.00189794541523, 0.00190131994382, 
0.00190471336763, 0.00190812583702, 0.00191155750401, 0.00191500852226, 
0.00191847904716, 0.00192196923578, 0.00192547924697, 0.00192900924132, 
0.00193255938122, 0.00193612983087, 0.00193972075632, 0.00194333232548, 
0.00194696470816, 0.00195061807608, 0.00195429260293, 0.00195798846434, 
0.00196170583797, 0.00196544490352, 0.00196920584273, 0.00197298883945, 
0.00197679407963, 0.00198062175139, 0.00198447204504, 0.0019883451531, 
0.00199224127032, 0.00199616059376, 0.00200010332279, 0.00200406965912, 
0.00200805980684, 0.00201207397248, 0.00201611236501, 0.00202017519591, 
0.00202426267917, 0.00202837503137, 0.00203251247167, 0.00203667522192, 
0.0020408635066, 0.00204507755298, 0.00204931759106, 0.00205358385367, 
0.00205787657648, 0.00206219599808, 0.00206654236, 0.00207091590675, 
0.0020753168859, 0.00207974554808, 0.00208420214707, 0.00208868693983, 
0.00209320018657, 0.00209774215075, 0.00210231309919, 0.00210691330211, 
0.00211154303315, 0.00211620256947, 0.00212089219178, 0.00212561218441, 
0.00213036283536, 0.00213514443635, 0.00213995728291, 0.00214480167443, 
0.00214967791421, 0.00215458630953, 0.00215952717173, 0.00216450081626, 
0.00216950756278, 0.00217454773517, 0.00217962166166, 0.00218472967488, 
0.00218987211194, 0.00219504931448, 0.00220026162879, 0.00220550940586, 
0.00221079300148, 0.00221611277629, 0.0022214690959, 0.00222686233097, 
0.00223229285726, 0.00223776105577, 0.00224326731282, 0.00224881202011, 
0.00225439557484, 0.00226001837983, 0.00226568084357, 0.00227138338037, 
0.00227712641041, 0.00228291035992, 0.0022887356612, 0.00229460275281, 
0.00230051207963, 0.00230646409301, 0.00231245925087, 0.0023184980178, 
0.00232458086525, 0.00233070827159, 0.00233688072225, 0.0023430987099, 
0.00234936273451, 0.00235567330357, 0.00236203093215, 0.00236843614311, 
0.00237488946721, 0.00238139144329, 0.00238794261838, 0.00239454354789, 
0.0024011947958, 0.00240789693476, 0.00241465054629, 0.00242145622099, 
0.00242831455864, 0.00243522616847, 0.00244219166926, 0.00244921168961, 
0.00245628686808, 0.00246341785339, 0.00247060530468, 0.00247784989167, 
0.00248515229487, 0.00249251320583, 0.00249993332737, 0.00250741337376, 
0.00251495407104, 0.00252255615716, 0.00253022038233, 0.0025379475092, 
0.00254573831317, 0.00255359358263, 0.00256151411925, 0.00256950073825, 
0.00257755426871, 0.00258567555384, 0.00259386545131, 0.00260212483355, 
0.00261045458806, 0.00261885561778, 0.00262732884136, 0.00263587519359, 
0.00264449562569, 0.00265319110571, 0.00266196261887, 0.00267081116801, 
0.00267973777393, 0.0026887434758, 0.00269782933163, 0.00270699641862, 
0.00271624583369, 0.00272557869385, 0.00273499613673, 0.00274449932104, 
0.00275408942703, 0.00276376765707, 0.00277353523609, 0.00278339341218, 
0.00279334345711, 0.0028033866669, 0.00281352436244, 0.00282375789002, 
0.00283408862203, 0.00284451795754, 0.00285504732298, 0.00286567817282, 
0.00287641199026, 0.00288725028794, 0.00289819460868, 0.00290924652627, 
0.00292040764622, 0.00293167960657, 0.00294306407875, 0.00295456276843, 
0.00296617741639, 0.00297790979945, 0.0029897617314, 0.00300173506401, 
0.00301383168798, 0.00302605353401, 0.00303840257386, 0.00305088082148, 
0.00306349033409, 0.00307623321343, 0.00308911160692, 0.00310212770895, 
0.00311528376217, 0.00312858205881, 0.00314202494211, 0.00315561480772, 
0.0031693541052, 0.00318324533954, 0.00319729107278, 0.00321149392561, 
0.00322585657908, 0.00324038177639, 0.00325507232467, 0.00326993109691, 
0.00328496103385, 0.00330016514607, 0.00331554651607, 0.00333110830039, 
0.00334685373195, 0.00336278612231, 0.00337890886413, 0.0033952254337, 
0.00341173939349, 0.0034284543949, 0.00344537418107, 0.00346250258978, 
0.00347984355648, 0.00349740111743, 0.003515179413, 0.00353318269104, 
0.0035514153104, 0.00356988174466, 0.00358858658586, 0.00360753454859, 
0.00362673047401, 0.00364617933423, 0.00366588623678, 0.00368585642927, 
0.00370609530423, 0.00372660840423, 0.00374740142715, 0.00376848023166, 
0.003789850843, 0.00381151945895, 0.00383349245613, 0.0038557763965, 
0.00387837803418, 0.00390130432261, 0.00392456242198, 0.003948159707, 
0.00397210377509, 0.00399640245485, 0.00402106381502, 0.00404609617378, 
0.00407150810852, 0.0040973084661, 0.00412350637355, 0.00415011124934, 
0.00417713281517, 0.00420458110833, 0.00423246649468, 0.00426079968232, 
0.00428959173587, 0.00431885409155, 0.00434859857299, 0.00437883740787, 
0.00440958324543, 0.00444084917489, 0.00447264874487, 0.00450499598384, 
0.00453790542166, 0.00457139211233, 0.00460547165794, 0.00464016023403, 
0.00467547461629, 0.00471143220883, 0.00474805107405, 0.00478534996422, 
0.00482334835495, 0.00486206648056, 0.00490152537162, 0.00494174689472, 
0.00498275379466, 0.00502456973923, 0.00506721936676, 0.00511072833663, 
0.00515512338308, 0.00520043237232, 0.00524668436343, 0.00529390967324, 
0.00534213994547, 0.00539140822453, 0.00544174903429, 0.00549319846226, 
0.00554579424961, 0.00559957588746, 0.00565458472007, 0.00571086405537, 
0.00576845928355, 0.00582741800439, 0.00588779016407, 0.00594962820229, 
0.00601298721066, 0.00607792510329, 0.00614450280088, 0.00621278442934, 
0.00628283753445, 0.00635473331407, 0.0064285468696, 0.00650435747851, 
0.00658224889015, 0.00666230964713, 0.00674463343484, 0.00682931946221, 
0.00691647287675, 0.00700620521785, 0.00709863491225, 0.00719388781647, 
0.0072920978115, 0.00739340745567, 0.00749796870249, 0.00760594369111, 
0.00771750561822, 0.00783283970125, 0.00795214424435, 0.00807563182005, 
0.00820353058174, 0.00833608572404, 0.00847356111093, 0.00861624109468, 
0.00876443255219, 0.00891846716958, 0.00907870401133, 0.00924553241611, 
0.00941937526894, 0.00960069270796, 0.00978998633497, 0.00998780401129, 
0.0101947453365, 0.0104114679261, 0.0106386946279, 0.0108772218446, 
0.0111279291666, 0.0113917905618, 0.0116698874246, 0.0119634238545, 
0.0122737446232, 0.0126023563976, 0.0129509529307, 0.0133214451123, 
0.013715997011, 0.0141370693493, 0.0145874722648, 0.0150704297552, 
0.0155896589436, 0.0161494682971, 0.0167548803038, 0.0174117860191, 
0.0181271415716, 0.0189092205398, 0.0197679416356, 0.0207152992546, 
0.0217659365933, 0.0229379195352, 0.0242537982861, 0.0257420895415, 
0.0274393867345, 0.0293934314855, 0.0316676970762, 0.0343484260987, 
0.0375557974315, 0.041462337604, 0.0463246817046, 0.0525414203953, 
0.0607656899311, 0.0721433019085, 0.0888734293534, 0.115733727009, 
0.165178011728};

static const double delta[2001]={
0.00907870401133, 0.00891846716958, 0.00876443255219, 0.00861624109468, 
0.00847356111093, 0.00833608572404, 0.00820353058174, 0.00807563182005, 
0.00795214424435, 0.00783283970125, 0.00771750561822, 0.00760594369111, 
0.00749796870249, 0.00739340745567, 0.0072920978115, 0.00719388781647, 
0.00709863491225, 0.00700620521785, 0.00691647287675, 0.00682931946221, 
0.00674463343484, 0.00666230964713, 0.00658224889015, 0.00650435747851, 
0.0064285468696, 0.00635473331407, 0.00628283753445, 0.00621278442934, 
0.00614450280088, 0.00607792510329, 0.00601298721066, 0.00594962820229, 
0.00588779016407, 0.00582741800439, 0.00576845928355, 0.00571086405537, 
0.00565458472007, 0.00559957588746, 0.00554579424961, 0.00549319846226, 
0.00544174903429, 0.00539140822453, 0.00534213994547, 0.00529390967324, 
0.00524668436343, 0.00520043237232, 0.00515512338308, 0.00511072833663, 
0.00506721936676, 0.00502456973923, 0.00498275379466, 0.00494174689472, 
0.00490152537162, 0.00486206648056, 0.00482334835495, 0.00478534996422, 
0.00474805107405, 0.00471143220883, 0.00467547461629, 0.00464016023403, 
0.00460547165794, 0.00457139211233, 0.00453790542166, 0.00450499598384, 
0.00447264874487, 0.00444084917489, 0.00440958324543, 0.00437883740787, 
0.00434859857299, 0.00431885409155, 0.00428959173587, 0.00426079968232, 
0.00423246649468, 0.00420458110833, 0.00417713281517, 0.00415011124934, 
0.00412350637355, 0.0040973084661, 0.00407150810852, 0.00404609617378, 
0.00402106381502, 0.00399640245485, 0.00397210377509, 0.003948159707, 
0.00392456242198, 0.00390130432261, 0.00387837803418, 0.0038557763965, 
0.00383349245613, 0.00381151945895, 0.003789850843, 0.00376848023166, 
0.00374740142715, 0.00372660840423, 0.00370609530423, 0.00368585642927, 
0.00366588623678, 0.00364617933423, 0.00362673047401, 0.00360753454859, 
0.00358858658586, 0.00356988174466, 0.0035514153104, 0.00353318269104, 
0.003515179413, 0.00349740111743, 0.00347984355648, 0.00346250258978, 
0.00344537418107, 0.0034284543949, 0.00341173939349, 0.0033952254337, 
0.00337890886413, 0.00336278612231, 0.00334685373195, 0.00333110830039, 
0.00331554651607, 0.00330016514607, 0.00328496103385, 0.00326993109691, 
0.00325507232467, 0.00324038177639, 0.00322585657908, 0.00321149392561, 
0.00319729107278, 0.00318324533954, 0.0031693541052, 0.00315561480772, 
0.00314202494211, 0.00312858205881, 0.00311528376217, 0.00310212770895, 
0.00308911160692, 0.00307623321343, 0.00306349033409, 0.00305088082148, 
0.00303840257386, 0.00302605353401, 0.00301383168798, 0.00300173506401, 
0.0029897617314, 0.00297790979945, 0.00296617741639, 0.00295456276843, 
0.00294306407875, 0.00293167960657, 0.00292040764622, 0.00290924652627, 
0.00289819460868, 0.00288725028794, 0.00287641199026, 0.00286567817282, 
0.00285504732298, 0.00284451795754, 0.00283408862203, 0.00282375789002, 
0.00281352436244, 0.0028033866669, 0.00279334345711, 0.00278339341218, 
0.00277353523609, 0.00276376765707, 0.00275408942703, 0.00274449932104, 
0.00273499613673, 0.00272557869385, 0.00271624583369, 0.00270699641862, 
0.00269782933163, 0.0026887434758, 0.00267973777393, 0.00267081116801, 
0.00266196261887, 0.00265319110571, 0.00264449562569, 0.00263587519359, 
0.00262732884136, 0.00261885561778, 0.00261045458806, 0.00260212483355, 
0.00259386545131, 0.00258567555384, 0.00257755426871, 0.00256950073825, 
0.00256151411925, 0.00255359358263, 0.00254573831317, 0.0025379475092, 
0.00253022038233, 0.00252255615716, 0.00251495407104, 0.00250741337376, 
0.00249993332737, 0.00249251320583, 0.00248515229487, 0.00247784989167, 
0.00247060530468, 0.00246341785339, 0.00245628686808, 0.00244921168961, 
0.00244219166926, 0.00243522616847, 0.00242831455864, 0.00242145622099, 
0.00241465054629, 0.00240789693476, 0.0024011947958, 0.00239454354789, 
0.00238794261838, 0.00238139144329, 0.00237488946721, 0.00236843614311, 
0.00236203093215, 0.00235567330356, 0.00234936273451, 0.0023430987099, 
0.00233688072225, 0.00233070827159, 0.00232458086525, 0.0023184980178, 
0.00231245925087, 0.00230646409301, 0.00230051207963, 0.00229460275281, 
0.0022887356612, 0.00228291035992, 0.00227712641041, 0.00227138338037, 
0.00226568084357, 0.00226001837983, 0.00225439557484, 0.00224881202011, 
0.00224326731282, 0.00223776105577, 0.00223229285726, 0.00222686233097, 
0.0022214690959, 0.00221611277629, 0.00221079300148, 0.00220550940586, 
0.00220026162879, 0.00219504931448, 0.00218987211194, 0.00218472967488, 
0.00217962166166, 0.00217454773517, 0.00216950756278, 0.00216450081626, 
0.00215952717173, 0.00215458630953, 0.00214967791421, 0.00214480167443, 
0.00213995728291, 0.00213514443635, 0.00213036283536, 0.00212561218441, 
0.00212089219178, 0.00211620256947, 0.00211154303315, 0.00210691330211, 
0.00210231309919, 0.00209774215075, 0.00209320018657, 0.00208868693983, 
0.00208420214707, 0.00207974554808, 0.0020753168859, 0.00207091590675, 
0.00206654236, 0.00206219599808, 0.00205787657648, 0.00205358385367, 
0.00204931759106, 0.00204507755298, 0.0020408635066, 0.00203667522192, 
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0.00126895143495, 0.00126937579041, 0.00126980247547, 0.00127023149523, 
0.00127066285481, 0.00127109655939, 0.00127153261415, 0.00127197102432, 
0.00127241179519, 0.00127285493205, 0.00127330044023, 0.00127374832512, 
0.00127419859212, 0.00127465124667, 0.00127510629426, 0.00127556374039, 
0.00127602359064, 0.00127648585057, 0.00127695052582, 0.00127741762206, 
0.00127788714497, 0.0012783591003, 0.00127883349382, 0.00127931033135, 
0.00127978961873, 0.00128027136184, 0.00128075556662, 0.00128124223903, 
0.00128173138507, 0.00128222301078, 0.00128271712224, 0.00128321372557, 
0.00128371282694, 0.00128421443253, 0.00128471854859, 0.00128522518139, 
0.00128573433726, 0.00128624602255, 0.00128676024366, 0.00128727700703, 
0.00128779631915, 0.00128831818653, 0.00128884261575, 0.0012893696134, 
0.00128989918614, 0.00129043134066, 0.00129096608368, 0.001291503422, 
0.00129204336242, 0.0012925859118, 0.00129313107706, 0.00129367886515, 
0.00129422928305, 0.00129478233781, 0.0012953380365, 0.00129589638626, 
0.00129645739425, 0.00129702106769, 0.00129758741385, 0.00129815644004, 
0.0012987281536, 0.00129930256194, 0.00129987967251, 0.0013004594928, 
0.00130104203035, 0.00130162729275, 0.00130221528764, 0.0013028060227, 
0.00130339950566, 0.00130399574431, 0.00130459474648, 0.00130519652004, 
0.00130580107292, 0.0013064084131, 0.0013070185486, 0.00130763148752, 
0.00130824723797, 0.00130886580813, 0.00130948720625, 0.00131011144059, 
0.00131073851949, 0.00131136845134, 0.00131200124458, 0.0013126369077, 
0.00131327544924, 0.00131391687781, 0.00131456120205, 0.00131520843067, 
0.00131585857243, 0.00131651163615, 0.00131716763069, 0.00131782656499, 
0.00131848844801, 0.00131915328881, 0.00131982109648, 0.00132049188016, 
0.00132116564906, 0.00132184241245, 0.00132252217966, 0.00132320496006, 
0.00132389076309, 0.00132457959826, 0.00132527147513, 0.00132596640331, 
0.00132666439248, 0.00132736545238, 0.00132806959281, 0.00132877682363, 
0.00132948715478, 0.00133020059622, 0.00133091715802, 0.00133163685028, 
0.00133235968317, 0.00133308566694, 0.00133381481189, 0.00133454712839, 
0.00133528262686, 0.0013360213178, 0.00133676321179, 0.00133750831944, 
0.00133825665146, 0.0013390082186, 0.00133976303171, 0.00134052110168, 
0.00134128243948, 0.00134204705614, 0.00134281496278, 0.00134358617057, 
0.00134436069075, 0.00134513853465, 0.00134591971366, 0.00134670423924, 
0.00134749212291, 0.0013482833763, 0.00134907801107, 0.00134987603898, 
0.00135067747187, 0.00135148232163, 0.00135229060024, 0.00135310231976, 
0.00135391749232, 0.00135473613013, 0.00135555824547, 0.00135638385071, 
0.00135721295829, 0.00135804558073, 0.00135888173063, 0.00135972142068, 
0.00136056466363, 0.00136141147233, 0.00136226185971, 0.00136311583877, 
0.00136397342261, 0.0013648346244, 0.0013656994574, 0.00136656793495, 
0.00136744007049, 0.00136831587753, 0.00136919536968, 0.00137007856062, 
0.00137096546413, 0.00137185609409, 0.00137275046444, 0.00137364858924, 
0.00137455048261, 0.0013754561588, 0.00137636563211, 0.00137727891696, 
0.00137819602786, 0.00137911697941, 0.0013800417863, 0.00138097046332, 
0.00138190302536, 0.0013828394874, 0.00138377986452, 0.0013847241719, 
0.00138567242482, 0.00138662463865, 0.00138758082887, 0.00138854101107, 
0.00138950520091, 0.00139047341419, 0.00139144566678, 0.00139242197469, 
0.00139340235401, 0.00139438682093, 0.00139537539178, 0.00139636808295, 
0.00139736491098, 0.00139836589251, 0.00139937104426, 0.00140038038311, 
0.001401393926, 0.00140241169003, 0.00140343369237, 0.00140445995035, 
0.00140549048136, 0.00140652530297, 0.00140756443281, 0.00140860788865, 
0.0014096556884, 0.00141070785004, 0.00141176439173, 0.0014128253317, 
0.00141389068833, 0.00141496048012, 0.00141603472569, 0.00141711344378, 
0.00141819665327, 0.00141928437316, 0.00142037662258, 0.00142147342079, 
0.00142257478717, 0.00142368074124, 0.00142479130266, 0.00142590649122, 
0.00142702632683, 0.00142815082955, 0.00142928001957, 0.00143041391723, 
0.00143155254299, 0.00143269591747, 0.00143384406141, 0.00143499699572, 
0.00143615474142, 0.0014373173197, 0.0014384847519, 0.00143965705947, 
0.00144083426406, 0.00144201638743, 0.0014432034515, 0.00144439547835, 
0.00144559249022, 0.00144679450948, 0.00144800155868, 0.00144921366051, 
0.00145043083783, 0.00145165311365, 0.00145288051115, 0.00145411305368, 
0.00145535076472, 0.00145659366796, 0.00145784178722, 0.00145909514651, 
0.00146035377001, 0.00146161768204, 0.00146288690714, 0.00146416146999, 
0.00146544139545, 0.00146672670856, 0.00146801743456, 0.00146931359882, 
0.00147061522694, 0.00147192234469, 0.001473234978, 0.00147455315301, 
0.00147587689605, 0.00147720623363, 0.00147854119245, 0.00147988179941, 
0.00148122808159, 0.00148258006629, 0.00148393778098, 0.00148530125335, 
0.00148667051128, 0.00148804558287, 0.0014894264964, 0.00149081328038, 
0.00149220596351, 0.0014936045747, 0.0014950091431, 0.00149641969805, 
0.0014978362691, 0.00149925888603, 0.00150068757885, 0.00150212237777, 
0.00150356331324, 0.00150501041593, 0.00150646371673, 0.00150792324678, 
0.00150938903744, 0.0015108611203, 0.00151233952719, 0.00151382429019, 
0.00151531544159, 0.00151681301397, 0.00151831704011, 0.00151982755306, 
0.00152134458612, 0.00152286817284, 0.00152439834701, 0.00152593514271, 
0.00152747859424, 0.00152902873619, 0.0015305856034, 0.00153214923099, 
0.00153371965432, 0.00153529690906, 0.00153688103112, 0.00153847205672, 
0.00154007002233, 0.00154167496471, 0.00154328692091, 0.00154490592827, 
0.00154653202442, 0.00154816524726, 0.00154980563502, 0.00155145322621, 
0.00155310805964, 0.00155477017442, 0.00155643960999, 0.00155811640608, 
0.00155980060273, 0.00156149224032, 0.00156319135953, 0.00156489800135, 
0.00156661220713, 0.00156833401853, 0.00157006347754, 0.00157180062648, 
0.00157354550803, 0.00157529816519, 0.00157705864132, 0.00157882698012, 
0.00158060322564, 0.0015823874223, 0.00158417961486, 0.00158597984847, 
0.00158778816861, 0.00158960462117, 0.00159142925237, 0.00159326210886, 
0.00159510323762, 0.00159695268604, 0.00159881050191, 0.0016006767334, 
0.00160255142907, 0.00160443463789, 0.00160632640925, 0.00160822679292, 
0.0016101358391, 0.00161205359842, 0.00161398012191, 0.00161591546103, 
0.0016178596677, 0.00161981279423, 0.00162177489341, 0.00162374601845, 
0.00162572622303, 0.00162771556126, 0.00162971408773, 0.00163172185748, 
0.00163373892603, 0.00163576534937, 0.00163780118397, 0.00163984648678, 
0.00164190131523, 0.00164396572728, 0.00164603978134, 0.00164812353636, 
0.00165021705179, 0.0016523203876, 0.00165443360428, 0.00165655676283, 
0.00165868992482, 0.00166083315233, 0.00166298650798, 0.00166515005497, 
0.00166732385702, 0.00166950797845, 0.00167170248412, 0.00167390743948, 
0.00167612291056, 0.00167834896397, 0.00168058566692, 0.00168283308723, 
0.00168509129331, 0.0016873603542, 0.00168964033956, 0.00169193131966, 
0.00169423336543, 0.00169654654844, 0.00169887094089, 0.00170120661566, 
0.00170355364628, 0.00170591210696, 0.00170828207259, 0.00171066361875, 
0.00171305682171, 0.00171546175844, 0.00171787850665, 0.00172030714473, 
0.00172274775183, 0.00172520040782, 0.00172766519333, 0.00173014218972, 
0.00173263147915, 0.00173513314452, 0.00173764726952, 0.00174017393865, 
0.00174271323718, 0.00174526525121, 0.00174783006766, 0.00175040777426, 
0.00175299845961, 0.00175560221311, 0.00175821912508, 0.00176084928666, 
0.00176349278989, 0.00176614972771, 0.00176882019394, 0.00177150428333, 
0.00177420209154, 0.00177691371518, 0.00177963925179, 0.00178237879988, 
0.00178513245892, 0.00178790032937, 0.00179068251268, 0.0017934791113, 
0.00179629022872, 0.00179911596944, 0.001801956439, 0.00180481174402, 
0.00180768199218, 0.00181056729223, 0.00181346775404, 0.00181638348858, 
0.00181931460795, 0.00182226122539, 0.00182522345529, 0.00182820141321, 
0.0018311952159, 0.00183420498131, 0.00183723082859, 0.00184027287815, 
0.00184333125163, 0.00184640607191, 0.0018494974632, 0.00185260555097, 
0.00185573046201, 0.00185887232445, 0.00186203126776, 0.00186520742277, 
0.00186840092171, 0.00187161189821, 0.00187484048732, 0.00187808682551, 
0.00188135105074, 0.00188463330243, 0.0018879337215, 0.00189125245041, 
0.00189458963314, 0.00189794541523, 0.00190131994382, 0.00190471336763, 
0.00190812583702, 0.00191155750401, 0.00191500852226, 0.00191847904716, 
0.00192196923578, 0.00192547924697, 0.00192900924132, 0.00193255938122, 
0.00193612983087, 0.00193972075632, 0.00194333232548, 0.00194696470816, 
0.00195061807608, 0.00195429260293, 0.00195798846434, 0.00196170583797, 
0.00196544490352, 0.00196920584273, 0.00197298883945, 0.00197679407963, 
0.00198062175139, 0.00198447204504, 0.0019883451531, 0.00199224127032, 
0.00199616059376, 0.00200010332279, 0.00200406965912, 0.00200805980684, 
0.00201207397248, 0.00201611236501, 0.00202017519591, 0.00202426267917, 
0.00202837503137, 0.00203251247167, 0.00203667522192, 0.0020408635066, 
0.00204507755298, 0.00204931759106, 0.00205358385367, 0.00205787657648, 
0.00206219599808, 0.00206654236, 0.00207091590675, 0.0020753168859, 
0.00207974554808, 0.00208420214707, 0.00208868693983, 0.00209320018657, 
0.00209774215075, 0.00210231309919, 0.00210691330211, 0.00211154303315, 
0.00211620256947, 0.00212089219178, 0.00212561218441, 0.00213036283536, 
0.00213514443635, 0.00213995728291, 0.00214480167443, 0.00214967791421, 
0.00215458630953, 0.00215952717173, 0.00216450081626, 0.00216950756278, 
0.00217454773517, 0.00217962166166, 0.00218472967488, 0.00218987211194, 
0.00219504931448, 0.00220026162879, 0.00220550940586, 0.00221079300148, 
0.00221611277629, 0.0022214690959, 0.00222686233097, 0.00223229285726, 
0.00223776105577, 0.00224326731282, 0.00224881202011, 0.00225439557484, 
0.00226001837983, 0.00226568084357, 0.00227138338037, 0.00227712641041, 
0.00228291035992, 0.0022887356612, 0.00229460275281, 0.00230051207963, 
0.00230646409301, 0.00231245925087, 0.0023184980178, 0.00232458086525, 
0.00233070827159, 0.00233688072225, 0.0023430987099, 0.00234936273451, 
0.00235567330356, 0.00236203093215, 0.00236843614311, 0.00237488946721, 
0.00238139144329, 0.00238794261838, 0.00239454354789, 0.0024011947958, 
0.00240789693476, 0.00241465054629, 0.00242145622099, 0.00242831455864, 
0.00243522616847, 0.00244219166926, 0.00244921168961, 0.00245628686808, 
0.00246341785339, 0.00247060530468, 0.00247784989167, 0.00248515229487, 
0.00249251320583, 0.00249993332737, 0.00250741337376, 0.00251495407104, 
0.00252255615716, 0.00253022038233, 0.0025379475092, 0.00254573831317, 
0.00255359358263, 0.00256151411925, 0.00256950073825, 0.00257755426871, 
0.00258567555384, 0.00259386545131, 0.00260212483355, 0.00261045458806, 
0.00261885561778, 0.00262732884136, 0.00263587519359, 0.00264449562569, 
0.00265319110571, 0.00266196261887, 0.00267081116801, 0.00267973777393, 
0.0026887434758, 0.00269782933163, 0.00270699641862, 0.00271624583369, 
0.00272557869385, 0.00273499613673, 0.00274449932104, 0.00275408942703, 
0.00276376765707, 0.00277353523609, 0.00278339341218, 0.00279334345711, 
0.0028033866669, 0.00281352436244, 0.00282375789002, 0.00283408862203, 
0.00284451795754, 0.00285504732298, 0.00286567817282, 0.00287641199026, 
0.00288725028794, 0.00289819460868, 0.00290924652627, 0.00292040764622, 
0.00293167960657, 0.00294306407875, 0.00295456276843, 0.00296617741639, 
0.00297790979945, 0.0029897617314, 0.00300173506401, 0.00301383168798, 
0.00302605353401, 0.00303840257386, 0.00305088082148, 0.00306349033409, 
0.00307623321343, 0.00308911160692, 0.00310212770895, 0.00311528376217, 
0.00312858205881, 0.00314202494211, 0.00315561480772, 0.0031693541052, 
0.00318324533954, 0.00319729107278, 0.00321149392561, 0.00322585657908, 
0.00324038177639, 0.00325507232467, 0.00326993109691, 0.00328496103385, 
0.00330016514607, 0.00331554651607, 0.00333110830039, 0.00334685373195, 
0.00336278612231, 0.00337890886413, 0.0033952254337, 0.00341173939349, 
0.0034284543949, 0.00344537418107, 0.00346250258978, 0.00347984355648, 
0.00349740111743, 0.003515179413, 0.00353318269104, 0.0035514153104, 
0.00356988174466, 0.00358858658586, 0.00360753454859, 0.00362673047401, 
0.00364617933423, 0.00366588623678, 0.00368585642927, 0.00370609530423, 
0.00372660840423, 0.00374740142715, 0.00376848023166, 0.003789850843, 
0.00381151945895, 0.00383349245613, 0.0038557763965, 0.00387837803418, 
0.00390130432261, 0.00392456242198, 0.003948159707, 0.00397210377509, 
0.00399640245485, 0.00402106381502, 0.00404609617378, 0.00407150810852, 
0.0040973084661, 0.00412350637355, 0.00415011124934, 0.00417713281517, 
0.00420458110833, 0.00423246649468, 0.00426079968232, 0.00428959173587, 
0.00431885409155, 0.00434859857299, 0.00437883740787, 0.00440958324543, 
0.00444084917489, 0.00447264874487, 0.00450499598384, 0.00453790542166, 
0.00457139211233, 0.00460547165794, 0.00464016023403, 0.00467547461629, 
0.00471143220883, 0.00474805107405, 0.00478534996422, 0.00482334835495, 
0.00486206648056, 0.00490152537162, 0.00494174689472, 0.00498275379466, 
0.00502456973923, 0.00506721936676, 0.00511072833663, 0.00515512338308, 
0.00520043237232, 0.00524668436343, 0.00529390967324, 0.00534213994547, 
0.00539140822453, 0.00544174903429, 0.00549319846226, 0.00554579424961, 
0.00559957588746, 0.00565458472007, 0.00571086405537, 0.00576845928355, 
0.00582741800439, 0.00588779016407, 0.00594962820229, 0.00601298721066, 
0.00607792510329, 0.00614450280088, 0.00621278442934, 0.00628283753445, 
0.00635473331407, 0.0064285468696, 0.00650435747851, 0.00658224889015, 
0.00666230964713, 0.00674463343484, 0.00682931946221, 0.00691647287675, 
0.00700620521785, 0.00709863491225, 0.00719388781647, 0.0072920978115, 
0.00739340745567, 0.00749796870249, 0.00760594369111, 0.00771750561822, 
0.00783283970125, 0.00795214424435, 0.00807563182005, 0.00820353058174, 
0.00833608572404, 0.00847356111093, 0.00861624109468, 0.00876443255219, 
0.00891846716958, 0.00907870401133, 0.00924553241611, 0.00941937526894, 
0.00960069270796, 0.00978998633497, 0.00998780401129, 0.0101947453365, 
0.0104114679261, 0.0106386946279, 0.0108772218446, 0.0111279291666, 
0.0113917905618, 0.0116698874246, 0.0119634238545, 0.0122737446232, 
0.0126023563976, 0.0129509529307, 0.0133214451123, 0.013715997011, 
0.0141370693493, 0.0145874722648, 0.0150704297552, 0.0155896589436, 
0.0161494682971, 0.0167548803038, 0.0174117860191, 0.0181271415716, 
0.0189092205398, 0.0197679416356, 0.0207152992546, 0.0217659365933, 
0.0229379195352, 0.0242537982861, 0.0257420895415, 0.0274393867345, 
0.0293934314855, 0.0316676970762, 0.0343484260987, 0.0375557974315, 
0.041462337604, 0.0463246817046, 0.0525414203953, 0.0607656899311, 
0.0721433019085, 0.0888734293534, 0.115733727009, 0.165178011728, 
0.280881510656};

static const unsigned short int ncell[3557]={
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 
2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 
5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 
8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 
11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 
15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 
18, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 22, 22, 
22, 22, 22, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 26, 
26, 26, 26, 26, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28, 29, 29, 29, 29, 29, 30, 
30, 30, 30, 30, 31, 31, 31, 31, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 34, 34, 
34, 34, 35, 35, 35, 35, 35, 36, 36, 36, 36, 36, 37, 37, 37, 37, 38, 38, 38, 38, 
38, 39, 39, 39, 39, 40, 40, 40, 40, 41, 41, 41, 41, 41, 42, 42, 42, 42, 43, 43, 
43, 43, 44, 44, 44, 44, 44, 45, 45, 45, 45, 46, 46, 46, 46, 47, 47, 47, 47, 48, 
48, 48, 48, 49, 49, 49, 49, 50, 50, 50, 50, 51, 51, 51, 51, 52, 52, 52, 52, 53, 
53, 53, 53, 54, 54, 54, 54, 55, 55, 55, 55, 56, 56, 56, 56, 57, 57, 57, 57, 58, 
58, 58, 59, 59, 59, 59, 60, 60, 60, 60, 61, 61, 61, 61, 62, 62, 62, 63, 63, 63, 
63, 64, 64, 64, 64, 65, 65, 65, 66, 66, 66, 66, 67, 67, 67, 68, 68, 68, 68, 69, 
69, 69, 70, 70, 70, 70, 71, 71, 71, 72, 72, 72, 72, 73, 73, 73, 74, 74, 74, 74, 
75, 75, 75, 76, 76, 76, 77, 77, 77, 77, 78, 78, 78, 79, 79, 79, 80, 80, 80, 81, 
81, 81, 81, 82, 82, 82, 83, 83, 83, 84, 84, 84, 85, 85, 85, 86, 86, 86, 86, 87, 
87, 87, 88, 88, 88, 89, 89, 89, 90, 90, 90, 91, 91, 91, 92, 92, 92, 93, 93, 93, 
94, 94, 94, 95, 95, 95, 96, 96, 96, 97, 97, 97, 98, 98, 98, 99, 99, 99, 100, 100, 
100, 101, 101, 101, 102, 102, 102, 103, 103, 104, 104, 104, 105, 105, 105, 106, 106, 106, 107, 107, 
107, 108, 108, 108, 109, 109, 110, 110, 110, 111, 111, 111, 112, 112, 112, 113, 113, 114, 114, 114, 
115, 115, 115, 116, 116, 117, 117, 117, 118, 118, 118, 119, 119, 120, 120, 120, 121, 121, 121, 122, 
122, 123, 123, 123, 124, 124, 124, 125, 125, 126, 126, 126, 127, 127, 128, 128, 128, 129, 129, 130, 
130, 130, 131, 131, 132, 132, 132, 133, 133, 134, 134, 134, 135, 135, 136, 136, 136, 137, 137, 138, 
138, 138, 139, 139, 140, 140, 140, 141, 141, 142, 142, 143, 143, 143, 144, 144, 145, 145, 145, 146, 
146, 147, 147, 148, 148, 148, 149, 149, 150, 150, 151, 151, 151, 152, 152, 153, 153, 154, 154, 154, 
155, 155, 156, 156, 157, 157, 157, 158, 158, 159, 159, 160, 160, 161, 161, 161, 162, 162, 163, 163, 
164, 164, 165, 165, 166, 166, 166, 167, 167, 168, 168, 169, 169, 170, 170, 171, 171, 171, 172, 172, 
173, 173, 174, 174, 175, 175, 176, 176, 177, 177, 177, 178, 178, 179, 179, 180, 180, 181, 181, 182, 
182, 183, 183, 184, 184, 185, 185, 186, 186, 187, 187, 188, 188, 189, 189, 189, 190, 190, 191, 191, 
192, 192, 193, 193, 194, 194, 195, 195, 196, 196, 197, 197, 198, 198, 199, 199, 200, 200, 201, 201, 
202, 202, 203, 203, 204, 204, 205, 205, 206, 206, 207, 208, 208, 209, 209, 210, 210, 211, 211, 212, 
212, 213, 213, 214, 214, 215, 215, 216, 216, 217, 217, 218, 218, 219, 220, 220, 221, 221, 222, 222, 
223, 223, 224, 224, 225, 225, 226, 226, 227, 228, 228, 229, 229, 230, 230, 231, 231, 232, 232, 233, 
234, 234, 235, 235, 236, 236, 237, 237, 238, 239, 239, 240, 240, 241, 241, 242, 242, 243, 244, 244, 
245, 245, 246, 246, 247, 248, 248, 249, 249, 250, 250, 251, 252, 252, 253, 253, 254, 254, 255, 256, 
256, 257, 257, 258, 258, 259, 260, 260, 261, 261, 262, 263, 263, 264, 264, 265, 266, 266, 267, 267, 
268, 269, 269, 270, 270, 271, 271, 272, 273, 273, 274, 274, 275, 276, 276, 277, 278, 278, 279, 279, 
280, 281, 281, 282, 282, 283, 284, 284, 285, 285, 286, 287, 287, 288, 289, 289, 290, 290, 291, 292, 
292, 293, 294, 294, 295, 295, 296, 297, 297, 298, 299, 299, 300, 300, 301, 302, 302, 303, 304, 304, 
305, 306, 306, 307, 307, 308, 309, 309, 310, 311, 311, 312, 313, 313, 314, 315, 315, 316, 317, 317, 
318, 318, 319, 320, 320, 321, 322, 322, 323, 324, 324, 325, 326, 326, 327, 328, 328, 329, 330, 330, 
331, 332, 332, 333, 334, 334, 335, 336, 336, 337, 338, 338, 339, 340, 340, 341, 342, 343, 343, 344, 
345, 345, 346, 347, 347, 348, 349, 349, 350, 351, 351, 352, 353, 354, 354, 355, 356, 356, 357, 358, 
358, 359, 360, 360, 361, 362, 363, 363, 364, 365, 365, 366, 367, 368, 368, 369, 370, 370, 371, 372, 
372, 373, 374, 375, 375, 376, 377, 377, 378, 379, 380, 380, 381, 382, 383, 383, 384, 385, 385, 386, 
387, 388, 388, 389, 390, 390, 391, 392, 393, 393, 394, 395, 396, 396, 397, 398, 399, 399, 400, 401, 
402, 402, 403, 404, 404, 405, 406, 407, 407, 408, 409, 410, 410, 411, 412, 413, 413, 414, 415, 416, 
416, 417, 418, 419, 419, 420, 421, 422, 423, 423, 424, 425, 426, 426, 427, 428, 429, 429, 430, 431, 
432, 432, 433, 434, 435, 436, 436, 437, 438, 439, 439, 440, 441, 442, 443, 443, 444, 445, 446, 446, 
447, 448, 449, 450, 450, 451, 452, 453, 453, 454, 455, 456, 457, 457, 458, 459, 460, 461, 461, 462, 
463, 464, 465, 465, 466, 467, 468, 469, 469, 470, 471, 472, 473, 473, 474, 475, 476, 477, 477, 478, 
479, 480, 481, 481, 482, 483, 484, 485, 485, 486, 487, 488, 489, 490, 490, 491, 492, 493, 494, 494, 
495, 496, 497, 498, 499, 499, 500, 501, 502, 503, 504, 504, 505, 506, 507, 508, 509, 509, 510, 511, 
512, 513, 514, 514, 515, 516, 517, 518, 519, 519, 520, 521, 522, 523, 524, 524, 525, 526, 527, 528, 
529, 529, 530, 531, 532, 533, 534, 535, 535, 536, 537, 538, 539, 540, 541, 541, 542, 543, 544, 545, 
546, 547, 547, 548, 549, 550, 551, 552, 553, 553, 554, 555, 556, 557, 558, 559, 559, 560, 561, 562, 
563, 564, 565, 566, 566, 567, 568, 569, 570, 571, 572, 573, 573, 574, 575, 576, 577, 578, 579, 580, 
580, 581, 582, 583, 584, 585, 586, 587, 587, 588, 589, 590, 591, 592, 593, 594, 595, 595, 596, 597, 
598, 599, 600, 601, 602, 603, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 612, 613, 614, 615, 
616, 617, 618, 619, 620, 621, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 631, 631, 632, 633, 
634, 635, 636, 637, 638, 639, 640, 641, 641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 
652, 653, 654, 655, 656, 657, 658, 659, 660, 661, 662, 663, 664, 664, 665, 666, 667, 668, 669, 670, 
671, 672, 673, 674, 675, 676, 677, 677, 678, 679, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 
690, 691, 692, 692, 693, 694, 695, 696, 697, 698, 699, 700, 701, 702, 703, 704, 705, 706, 707, 708, 
708, 709, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 720, 721, 722, 723, 724, 725, 726, 727, 
727, 728, 729, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 740, 741, 742, 743, 744, 745, 746, 
747, 748, 749, 749, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 760, 761, 762, 763, 764, 765, 
766, 767, 768, 769, 770, 771, 772, 773, 774, 775, 776, 777, 778, 778, 779, 780, 781, 782, 783, 784, 
785, 786, 787, 788, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 800, 801, 802, 803, 804, 
805, 806, 807, 808, 809, 810, 811, 812, 813, 814, 815, 816, 817, 818, 818, 819, 820, 821, 822, 823, 
824, 825, 826, 827, 828, 829, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 843, 
844, 845, 846, 847, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 860, 861, 862, 863, 
864, 865, 866, 867, 868, 869, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 880, 881, 882, 883, 
884, 885, 886, 887, 888, 889, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 900, 901, 902, 903, 
904, 905, 906, 907, 908, 909, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 920, 921, 922, 923, 
924, 925, 926, 927, 928, 929, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 940, 941, 942, 943, 
944, 945, 946, 947, 948, 949, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 960, 961, 962, 963, 
964, 965, 966, 967, 968, 969, 970, 971, 972, 973, 974, 975, 976, 977, 978, 978, 979, 980, 981, 982, 
983, 984, 985, 986, 987, 988, 989, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999, 1000, 1001, 1002, 
1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 1020, 1021, 1022, 
1023, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 1040, 1041, 1042, 
1043, 1044, 1045, 1046, 1047, 1048, 1049, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 1060, 1061, 1062, 
1063, 1064, 1065, 1066, 1067, 1068, 1069, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 1080, 1081, 1082, 
1083, 1084, 1085, 1086, 1087, 1088, 1089, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 1100, 1101, 1102, 
1103, 1104, 1105, 1106, 1107, 1108, 1109, 1110, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 1120, 1121, 1122, 
1123, 1124, 1125, 1126, 1127, 1128, 1129, 1130, 1131, 1132, 1133, 1134, 1135, 1135, 1136, 1137, 1138, 1139, 1140, 1141, 
1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 1160, 1161, 
1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 1170, 1171, 1172, 1173, 1174, 1175, 1175, 1176, 1177, 1178, 1179, 1180, 
1181, 1182, 1183, 1184, 1185, 1186, 1187, 1188, 1189, 1190, 1191, 1192, 1193, 1194, 1195, 1196, 1197, 1198, 1199, 1200, 
1201, 1202, 1203, 1204, 1204, 1205, 1206, 1207, 1208, 1209, 1210, 1211, 1212, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 
1220, 1221, 1222, 1223, 1224, 1225, 1226, 1226, 1227, 1228, 1229, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1237, 1238, 
1239, 1240, 1241, 1242, 1243, 1244, 1245, 1245, 1246, 1247, 1248, 1249, 1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257, 
1258, 1259, 1260, 1261, 1261, 1262, 1263, 1264, 1265, 1266, 1267, 1268, 1269, 1270, 1271, 1272, 1273, 1274, 1275, 1276, 
1276, 1277, 1278, 1279, 1280, 1281, 1282, 1283, 1284, 1285, 1286, 1287, 1288, 1289, 1289, 1290, 1291, 1292, 1293, 1294, 
1295, 1296, 1297, 1298, 1299, 1300, 1301, 1301, 1302, 1303, 1304, 1305, 1306, 1307, 1308, 1309, 1310, 1311, 1312, 1312, 
1313, 1314, 1315, 1316, 1317, 1318, 1319, 1320, 1321, 1322, 1322, 1323, 1324, 1325, 1326, 1327, 1328, 1329, 1330, 1331, 
1332, 1332, 1333, 1334, 1335, 1336, 1337, 1338, 1339, 1340, 1341, 1341, 1342, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 
1350, 1350, 1351, 1352, 1353, 1354, 1355, 1356, 1357, 1358, 1358, 1359, 1360, 1361, 1362, 1363, 1364, 1365, 1366, 1366, 
1367, 1368, 1369, 1370, 1371, 1372, 1373, 1373, 1374, 1375, 1376, 1377, 1378, 1379, 1380, 1380, 1381, 1382, 1383, 1384, 
1385, 1386, 1387, 1387, 1388, 1389, 1390, 1391, 1392, 1393, 1394, 1394, 1395, 1396, 1397, 1398, 1399, 1400, 1400, 1401, 
1402, 1403, 1404, 1405, 1406, 1406, 1407, 1408, 1409, 1410, 1411, 1412, 1412, 1413, 1414, 1415, 1416, 1417, 1418, 1418, 
1419, 1420, 1421, 1422, 1423, 1424, 1424, 1425, 1426, 1427, 1428, 1429, 1429, 1430, 1431, 1432, 1433, 1434, 1434, 1435, 
1436, 1437, 1438, 1439, 1439, 1440, 1441, 1442, 1443, 1444, 1444, 1445, 1446, 1447, 1448, 1449, 1449, 1450, 1451, 1452, 
1453, 1454, 1454, 1455, 1456, 1457, 1458, 1459, 1459, 1460, 1461, 1462, 1463, 1463, 1464, 1465, 1466, 1467, 1468, 1468, 
1469, 1470, 1471, 1472, 1472, 1473, 1474, 1475, 1476, 1476, 1477, 1478, 1479, 1480, 1480, 1481, 1482, 1483, 1484, 1484, 
1485, 1486, 1487, 1488, 1488, 1489, 1490, 1491, 1492, 1492, 1493, 1494, 1495, 1496, 1496, 1497, 1498, 1499, 1500, 1500, 
1501, 1502, 1503, 1503, 1504, 1505, 1506, 1507, 1507, 1508, 1509, 1510, 1510, 1511, 1512, 1513, 1514, 1514, 1515, 1516, 
1517, 1517, 1518, 1519, 1520, 1521, 1521, 1522, 1523, 1524, 1524, 1525, 1526, 1527, 1527, 1528, 1529, 1530, 1530, 1531, 
1532, 1533, 1534, 1534, 1535, 1536, 1537, 1537, 1538, 1539, 1540, 1540, 1541, 1542, 1543, 1543, 1544, 1545, 1546, 1546, 
1547, 1548, 1549, 1549, 1550, 1551, 1551, 1552, 1553, 1554, 1554, 1555, 1556, 1557, 1557, 1558, 1559, 1560, 1560, 1561, 
1562, 1563, 1563, 1564, 1565, 1565, 1566, 1567, 1568, 1568, 1569, 1570, 1570, 1571, 1572, 1573, 1573, 1574, 1575, 1576, 
1576, 1577, 1578, 1578, 1579, 1580, 1581, 1581, 1582, 1583, 1583, 1584, 1585, 1585, 1586, 1587, 1588, 1588, 1589, 1590, 
1590, 1591, 1592, 1593, 1593, 1594, 1595, 1595, 1596, 1597, 1597, 1598, 1599, 1599, 1600, 1601, 1602, 1602, 1603, 1604, 
1604, 1605, 1606, 1606, 1607, 1608, 1608, 1609, 1610, 1610, 1611, 1612, 1613, 1613, 1614, 1615, 1615, 1616, 1617, 1617, 
1618, 1619, 1619, 1620, 1621, 1621, 1622, 1623, 1623, 1624, 1625, 1625, 1626, 1627, 1627, 1628, 1629, 1629, 1630, 1631, 
1631, 1632, 1633, 1633, 1634, 1635, 1635, 1636, 1636, 1637, 1638, 1638, 1639, 1640, 1640, 1641, 1642, 1642, 1643, 1644, 
1644, 1645, 1646, 1646, 1647, 1647, 1648, 1649, 1649, 1650, 1651, 1651, 1652, 1653, 1653, 1654, 1654, 1655, 1656, 1656, 
1657, 1658, 1658, 1659, 1659, 1660, 1661, 1661, 1662, 1663, 1663, 1664, 1664, 1665, 1666, 1666, 1667, 1668, 1668, 1669, 
1669, 1670, 1671, 1671, 1672, 1672, 1673, 1674, 1674, 1675, 1675, 1676, 1677, 1677, 1678, 1679, 1679, 1680, 1680, 1681, 
1682, 1682, 1683, 1683, 1684, 1684, 1685, 1686, 1686, 1687, 1687, 1688, 1689, 1689, 1690, 1690, 1691, 1692, 1692, 1693, 
1693, 1694, 1695, 1695, 1696, 1696, 1697, 1697, 1698, 1699, 1699, 1700, 1700, 1701, 1701, 1702, 1703, 1703, 1704, 1704, 
1705, 1705, 1706, 1707, 1707, 1708, 1708, 1709, 1709, 1710, 1711, 1711, 1712, 1712, 1713, 1713, 1714, 1714, 1715, 1716, 
1716, 1717, 1717, 1718, 1718, 1719, 1719, 1720, 1721, 1721, 1722, 1722, 1723, 1723, 1724, 1724, 1725, 1725, 1726, 1727, 
1727, 1728, 1728, 1729, 1729, 1730, 1730, 1731, 1731, 1732, 1732, 1733, 1733, 1734, 1735, 1735, 1736, 1736, 1737, 1737, 
1738, 1738, 1739, 1739, 1740, 1740, 1741, 1741, 1742, 1742, 1743, 1743, 1744, 1744, 1745, 1745, 1746, 1747, 1747, 1748, 
1748, 1749, 1749, 1750, 1750, 1751, 1751, 1752, 1752, 1753, 1753, 1754, 1754, 1755, 1755, 1756, 1756, 1757, 1757, 1758, 
1758, 1759, 1759, 1760, 1760, 1761, 1761, 1762, 1762, 1763, 1763, 1764, 1764, 1764, 1765, 1765, 1766, 1766, 1767, 1767, 
1768, 1768, 1769, 1769, 1770, 1770, 1771, 1771, 1772, 1772, 1773, 1773, 1774, 1774, 1775, 1775, 1776, 1776, 1776, 1777, 
1777, 1778, 1778, 1779, 1779, 1780, 1780, 1781, 1781, 1782, 1782, 1782, 1783, 1783, 1784, 1784, 1785, 1785, 1786, 1786, 
1787, 1787, 1787, 1788, 1788, 1789, 1789, 1790, 1790, 1791, 1791, 1792, 1792, 1792, 1793, 1793, 1794, 1794, 1795, 1795, 
1796, 1796, 1796, 1797, 1797, 1798, 1798, 1799, 1799, 1799, 1800, 1800, 1801, 1801, 1802, 1802, 1802, 1803, 1803, 1804, 
1804, 1805, 1805, 1805, 1806, 1806, 1807, 1807, 1808, 1808, 1808, 1809, 1809, 1810, 1810, 1810, 1811, 1811, 1812, 1812, 
1813, 1813, 1813, 1814, 1814, 1815, 1815, 1815, 1816, 1816, 1817, 1817, 1817, 1818, 1818, 1819, 1819, 1819, 1820, 1820, 
1821, 1821, 1821, 1822, 1822, 1823, 1823, 1823, 1824, 1824, 1825, 1825, 1825, 1826, 1826, 1827, 1827, 1827, 1828, 1828, 
1829, 1829, 1829, 1830, 1830, 1830, 1831, 1831, 1832, 1832, 1832, 1833, 1833, 1833, 1834, 1834, 1835, 1835, 1835, 1836, 
1836, 1836, 1837, 1837, 1838, 1838, 1838, 1839, 1839, 1839, 1840, 1840, 1841, 1841, 1841, 1842, 1842, 1842, 1843, 1843, 
1843, 1844, 1844, 1845, 1845, 1845, 1846, 1846, 1846, 1847, 1847, 1847, 1848, 1848, 1848, 1849, 1849, 1849, 1850, 1850, 
1851, 1851, 1851, 1852, 1852, 1852, 1853, 1853, 1853, 1854, 1854, 1854, 1855, 1855, 1855, 1856, 1856, 1856, 1857, 1857, 
1857, 1858, 1858, 1858, 1859, 1859, 1859, 1860, 1860, 1860, 1861, 1861, 1861, 1862, 1862, 1862, 1863, 1863, 1863, 1864, 
1864, 1864, 1865, 1865, 1865, 1866, 1866, 1866, 1867, 1867, 1867, 1867, 1868, 1868, 1868, 1869, 1869, 1869, 1870, 1870, 
1870, 1871, 1871, 1871, 1872, 1872, 1872, 1872, 1873, 1873, 1873, 1874, 1874, 1874, 1875, 1875, 1875, 1876, 1876, 1876, 
1876, 1877, 1877, 1877, 1878, 1878, 1878, 1879, 1879, 1879, 1879, 1880, 1880, 1880, 1881, 1881, 1881, 1881, 1882, 1882, 
1882, 1883, 1883, 1883, 1883, 1884, 1884, 1884, 1885, 1885, 1885, 1885, 1886, 1886, 1886, 1887, 1887, 1887, 1887, 1888, 
1888, 1888, 1889, 1889, 1889, 1889, 1890, 1890, 1890, 1890, 1891, 1891, 1891, 1892, 1892, 1892, 1892, 1893, 1893, 1893, 
1893, 1894, 1894, 1894, 1894, 1895, 1895, 1895, 1896, 1896, 1896, 1896, 1897, 1897, 1897, 1897, 1898, 1898, 1898, 1898, 
1899, 1899, 1899, 1899, 1900, 1900, 1900, 1900, 1901, 1901, 1901, 1901, 1902, 1902, 1902, 1902, 1903, 1903, 1903, 1903, 
1904, 1904, 1904, 1904, 1905, 1905, 1905, 1905, 1906, 1906, 1906, 1906, 1907, 1907, 1907, 1907, 1908, 1908, 1908, 1908, 
1909, 1909, 1909, 1909, 1909, 1910, 1910, 1910, 1910, 1911, 1911, 1911, 1911, 1912, 1912, 1912, 1912, 1912, 1913, 1913, 
1913, 1913, 1914, 1914, 1914, 1914, 1915, 1915, 1915, 1915, 1915, 1916, 1916, 1916, 1916, 1917, 1917, 1917, 1917, 1917, 
1918, 1918, 1918, 1918, 1918, 1919, 1919, 1919, 1919, 1920, 1920, 1920, 1920, 1920, 1921, 1921, 1921, 1921, 1921, 1922, 
1922, 1922, 1922, 1923, 1923, 1923, 1923, 1923, 1924, 1924, 1924, 1924, 1924, 1925, 1925, 1925, 1925, 1925, 1926, 1926, 
1926, 1926, 1926, 1927, 1927, 1927, 1927, 1927, 1928, 1928, 1928, 1928, 1928, 1929, 1929, 1929, 1929, 1929, 1929, 1930, 
1930, 1930, 1930, 1930, 1931, 1931, 1931, 1931, 1931, 1932, 1932, 1932, 1932, 1932, 1933, 1933, 1933, 1933, 1933, 1933, 
1934, 1934, 1934, 1934, 1934, 1935, 1935, 1935, 1935, 1935, 1935, 1936, 1936, 1936, 1936, 1936, 1936, 1937, 1937, 1937, 
1937, 1937, 1938, 1938, 1938, 1938, 1938, 1938, 1939, 1939, 1939, 1939, 1939, 1939, 1940, 1940, 1940, 1940, 1940, 1940, 
1941, 1941, 1941, 1941, 1941, 1941, 1942, 1942, 1942, 1942, 1942, 1942, 1943, 1943, 1943, 1943, 1943, 1943, 1944, 1944, 
1944, 1944, 1944, 1944, 1944, 1945, 1945, 1945, 1945, 1945, 1945, 1946, 1946, 1946, 1946, 1946, 1946, 1947, 1947, 1947, 
1947, 1947, 1947, 1947, 1948, 1948, 1948, 1948, 1948, 1948, 1948, 1949, 1949, 1949, 1949, 1949, 1949, 1949, 1950, 1950, 
1950, 1950, 1950, 1950, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1951, 1952, 1952, 1952, 1952, 1952, 1952, 1952, 1953, 
1953, 1953, 1953, 1953, 1953, 1953, 1954, 1954, 1954, 1954, 1954, 1954, 1954, 1955, 1955, 1955, 1955, 1955, 1955, 1955, 
1955, 1956, 1956, 1956, 1956, 1956, 1956, 1956, 1956, 1957, 1957, 1957, 1957, 1957, 1957, 1957, 1958, 1958, 1958, 1958, 
1958, 1958, 1958, 1958, 1959, 1959, 1959, 1959, 1959, 1959, 1959, 1959, 1959, 1960, 1960, 1960, 1960, 1960, 1960, 1960, 
1960, 1961, 1961, 1961, 1961, 1961, 1961, 1961, 1961, 1962, 1962, 1962, 1962, 1962, 1962, 1962, 1962, 1962, 1963, 1963, 
1963, 1963, 1963, 1963, 1963, 1963, 1963, 1964, 1964, 1964, 1964, 1964, 1964, 1964, 1964, 1964, 1965, 1965, 1965, 1965, 
1965, 1965, 1965, 1965, 1965, 1966, 1966, 1966, 1966, 1966, 1966, 1966, 1966, 1966, 1966, 1967, 1967, 1967, 1967, 1967, 
1967, 1967, 1967, 1967, 1967, 1968, 1968, 1968, 1968, 1968, 1968, 1968, 1968, 1968, 1968, 1969, 1969, 1969, 1969, 1969, 
1969, 1969, 1969, 1969, 1969, 1970, 1970, 1970, 1970, 1970, 1970, 1970, 1970, 1970, 1970, 1971, 1971, 1971, 1971, 1971, 
1971, 1971, 1971, 1971, 1971, 1971, 1972, 1972, 1972, 1972, 1972, 1972, 1972, 1972, 1972, 1972, 1972, 1973, 1973, 1973, 
1973, 1973, 1973, 1973, 1973, 1973, 1973, 1973, 1973, 1974, 1974, 1974, 1974, 1974, 1974, 1974, 1974, 1974, 1974, 1974, 
1974, 1975, 1975, 1975, 1975, 1975, 1975, 1975, 1975, 1975, 1975, 1975, 1975, 1976, 1976, 1976, 1976, 1976, 1976, 1976, 
1976, 1976, 1976, 1976, 1976, 1976, 1977, 1977, 1977, 1977, 1977, 1977, 1977, 1977, 1977, 1977, 1977, 1977, 1977, 1978, 
1978, 1978, 1978, 1978, 1978, 1978, 1978, 1978, 1978, 1978, 1978, 1978, 1978, 1979, 1979, 1979, 1979, 1979, 1979, 1979, 
1979, 1979, 1979, 1979, 1979, 1979, 1979, 1980, 1980, 1980, 1980, 1980, 1980, 1980, 1980, 1980, 1980, 1980, 1980, 1980, 
1980, 1980, 1981, 1981, 1981, 1981, 1981, 1981, 1981, 1981, 1981, 1981, 1981, 1981, 1981, 1981, 1981};

    //****************************************
    // already #defined: N, I0, INVH, AMIN, AMAX
    #define ALPHA 1.83787706641  // = log(2*pi)
    double sim, simy, u;
    int k, ka, i;
    
    if (a<AMIN)  //if a is too small, use simple reject algorithm
        return ran_tg_reject(r,a);
    
    if (a>AMAX) // if a is too large, use Devroye's algorithm
        return ran_tg_devroye(r,a);

    i = I0+floor(a*INVH);
    ka = ncell[i];
    do {
      // sample integer between ka and N 
        k = ka+gsl_rng_uniform_int(r,N-ka+1); 
        if (k==N)  //right tail (last box on the right) 
                return ran_tg_devroye(r,x[N]); 
        if (k>ka+1)  {   // all the other boxes
            u = gsl_rng_uniform(r);
            simy = yu[k]*u;
            if (simy<yl[k]) { // that's what happens most of the time 
                sim = x[k]+u*delta[k];
                return sim;
            }
            // otherwise, check you're below the pdf curve
            sim = x[k]+d[k]*gsl_rng_uniform(r);
            if (sim*sim+2.*log(simy)+ALPHA<0.)
                return sim;
        }
	else {  // two leftmost regions 
            sim = x[k]+d[k]*gsl_rng_uniform(r);
            if (sim>=a) { //otherwise reject
                simy = yu[k]*gsl_rng_uniform(r);
                if (simy<yl[k])
                    return sim;
                if (sim*sim+2.*log(simy)+ALPHA<0.)
                    return sim;
                }
	}
    }
    while(1);

}


